This is a great question with a lot of thorny information in it. I'll try to be as specific as possible, and use those specifics to talk about some generalities, but let me go through your questions one by one.

1 - depending on the time frame/year of enlistment will I be more than likely stationed in the South to guard the Reconstruction process or would I be sent to the frontier to fight the natives?

We have to break this one into two parts. First, timeframe and second, your assignment.

Timeframe is a big one. There were more than a million men in the Union Army in 1865, which was reduced down to 26,312 by 1876. Most of those million men had been mustered in state volunteer regiments, with the regulars comprising only ~56,000 by 1867, but even that took a deliberate recruitment effort to fill; at one point after the Civil War ended, the US army was 20,000 men short of it's legally authorized size. Competition for officer positions was extremely high, but the turnover rates of enlisted men meant that recruiting was a big problem for the entire period, and it was likely that with a little work you'd be able to find a recruiter and sign up.

Your assignment was going to depend largely on your regiment (which I'll get to in question #2, below), but if you managed to enlist just after the war, there's a fair chance that you'd serve in the south. In 1867, of the 53,815 men in the regulars, 20,117 men were serving in some capacity in the American south in a Reconstruction capacity. By 1876, only roughly 6,000 out of the 26,000 men in the army were serving in the south. By 1877, Reconstruction was ended, and there were vanishingly few roles apart from garrison duties as normal on the east coast.

Apart from Reconstruction, regular duties in the West took up the bulk of the Army's activity. The Division of the Atlantic would generally see maybe a quarter of the mustered force of the United States stationed there in garrison duties, but regiments and companies went through a rotation, in which certain units would serve in the west and rotate back to the east after a number of years. But even being stationed out west, the chances of you engaging with any regularity in combat would be fairly slim. To quote Gregory Urwin in The United States Infantry, where most of this information comes from:

From 1865 to 1898, he US Army conducted 938 combat actions against hostile warriors, encounters resulting in the deaths of 919 Bluecoats and the wounding of 1,025 more.

Fairly slim chances, but that didn't mean it was impossible. Still, it was statistically likely that, if you enlisted to a term of five years (the standard) after 1876, you'd spend some of your enlistment in the west.

2 - during enlistment could I "choose" which unit I wanted to be in as in modern times you can "choose" your MOS/army role, say for instance instead of being in the infantry I wanted to be in the calvary?

Yes, but not in the way that you can today. Your enlistment would basically be a direct agreement with your regiment. Lt. Calvin Cowles of the 23rd Regiment of Infantry, for instance, was assigned by his company to recruit in New York, while his company was stationed at Fort Mackinac, Michigan. If you talked to Lt. Cowles, you'd be brought in to serve his regiment, and possibly his company or at least his post; you'd have choices only if your previous occupation gave you special skills (say, as a tailor or barber), or if you could find recruiters for other regiments with the job you wanted. Cowles might, however, direct you to a cavalry recruiter if you had a history of riding, but that wasn't at all a guarantee.

There was no large-scale basic training in the sense that we know today. There were, sometimes, recruitment depots or processing posts, where you'd learn the absolute basics, but for the most part you'd be transported to your regiment's post, and you'd be trained on the job.

3 - If I am stationed out West or in the South what would my daily duties be like and how would they compare or contrast with each other?

Let me be totally clear on this: your average every day duties on a regular military post in the latter half of the 19th century would be unbelievable drudgery. The post itself would need to be maintained, which could vary between repainting permanent buildings to pitching tents (which in some western posts were all the buildings they had). Latrines had to be cleaned, fuel had to be purchased or collected, supplies had to be escorted in, sorted, stowed, or maintained, kitchen duties and sentry duties were on a rotation. If you were in hostile territory (whether that was the American south or the West), patrols were organized and rotated. There was daily drill, semi-monthly inspections and parades, marksmanship practice (sometimes at some posts and generally not regularly until the early 1880s). If you were an artilleryman, practice would involve "running out" the gun, dummy-firing and practicing the dry execution of loading and cleaning your gun. If you were firing, it might involve literally hitching up and marching your cannons away from any nearby towns so you didn't risk accidentally hitting civilian buildings. The Fort Mackinac post had to drag their guns down a 150 foot hill and thereafter to a spot away from the town that didn't fire into shipping lanes, and then had to drag it back at the end of the day. At one point, the commandant decided to build a storehouse to store the cannons, but it had to be guarded, and the guards kept slipping away to get drunk, so they said forget it and went back to dragging the guns around.

You are at the beck and call of your officers 24 hours a day, 7 days a week. If you're lucky, your post has a good rapport with the surrounding area or any nearby towns, and you can have a night off every now and again to socialize. You might have a baseball team or a rifle team. You are never allowed to wear anything other than approved regulation issue clothing to prevent easy desertion. Drinking on most posts is not allowed. You have to purchase basic necessities from the post exchange, which might be marked up tremendously if your post is away from population centers.

You're paid $13 a month, as a private (pay for volunteer privates in the Civil War started at $16) There's no such thing as hazard pay. You get raises as you get promoted, which is more or less guaranteed unless you're regularly drunk, regularly AWOL, desert, or get into frequent trouble with your superiors. One soldier in the 1880s, Amos Wilkie, stationed at the relative resort town of Mackinac Island, was court-martialed seven times in his four years at Mackinac, almost half of which was due to insubordination to superior officers. At one point, he is recorded as saying to Corporal William Williams: "I won't clean out that pig pen for you, or any other man, Williams!" and then to the sergeant of the work detail, who warned Wilkie that if he didn't obey orders he'd be arrested and court-martialed: "I won't clean out that pig pen, and you can do as you please!"

Wilkie was arrested, court-martialed, and sentenced to forfeit his entire month's pay, and serve at hard labor under the charge of the guard for 30 days. Both were remanded down to half the sentence, $7 and 15 days hard labor. To put this kind of troublemaking into perspective, when Wilkie was discharged in 1891 (after his unit rotated out to Texas), he was noted as having "good behavior."

Even for soldiers of a better comportment, the work was soul-crushing, and never-ending. White regiments, however, could at least look forward to rotating out of the west, and possibly to places like Mackinac, or forts near Chicago, Detroit, New York, etc, where life would be easy, social, and accessible. Not so for Buffalo Soldier regiments, who stayed at miserable, lonely posts like Fort Snelling for their entire service duration. Black regiments, paradoxically, typically had much lower desertion rates, had more soldiers with more individual experience than most other companies in the entire US Army, and quite a few had combat experience, as well. Interesting as that disparity is, it's somewhat beyond the scope of the question. So too is the discussion of army wives, whose experience was summed up as "glittering misery." Please ask a follow-up about either of these!

4 - What would the social standing for a man of my background be in the Army?

Let's just say you're unlikely to be thanked for your service. The cultural beliefs about armies was very negative; it was believed that men in any standing army were slothful troublemakers who couldn't find better work elsewhere. If they could, they wouldn't be in the army! They were poorly paid, policed like hawks, and when they let off steam it was usually at the direct expense of the citizenry, the citizenry's daughters, or publicans and merchants. They liked to drink, fight, and find time for women of any description. Officers were different, as officership was at least believed to be a suitable profession for a young man; West Point had a sterling reputation not just as a military academy, but as an engineering school and many young officers looked to pad their resume for their eventual transition to civilian life as an engineer.

But as an enlisted man? Your social standing is as close to the bottom as it could be. It was worse as an immigrant.

5 - How dangerous will this new line of work be compared to staying home in backbreaking poverty?

This is likely more a matter of opinion than otherwise. See above: does this sound like a great job? How might it differ from a non-union miner in a company town? There were times and places that being a soldier would be very dangerous - ask the 2,000 men killed or wounded mentioned above - but there are also times when it would have been much more dangerous to be a miner. Compared to poverty? Well, you'll be better fed, at least.