Or would I only be able to buy a couple of fancy-pants items but still be considered a filthy peasant by even the pettiest of lords?
For the purposes of this answer, let's say you've ended up in England before the 12th Century. Your first problem is going to be working out what to do with the gold coins: what is their weight and value? The workhorse of the Medieval English economy was the silver penny: there were 12d in a shilling (4 if you were Mercian) and 240d in a pound, but these latter values were measures of worth, not circulating coins. The mancus was both a measure of value and (occasionally) a gold coin, and was valued at 30d. While mancus coins did exist, they appear to have been predominantly ceremonial or celebratory issues rather than designed for use as everyday coinage.
To start with, let's hope you've brought actual gold coins. Early medieval English coinage was rigorously policed for its Troy grain weight and its consistency while modern coinage is largely symbolic: modern 'silver' coins are mostly nickel-plated steel, for example. If you were found to be trying to defraud the Exchequer by passing undervalued coinage, you were liable to get your hand chopped off (as per Æthelstan II Grately). If you had 100 Krugerands, with their distinctive 1 Troy ounce of gold, I might ask why you'd want to return to the 11th Century, since you'd have about £170,000 in your pocket based on current valuation, whereas in terms of the more literal valuation of Early Medieval coinage, this would provide you with starting capital of some 6L, 60d, assuming that you could find a fair exchange. Let's assume on the other hand that your gold coins are analogous to the dinar or the mancus and accepted at face value without being restamped; 100 mancuses would fetch you a more substantial 12L 10s.
These are not necessarily insubstantial sums; the 6L 60d from your temporially displaced Krugerrands would allow you to buy 4 horses, for example (valued at 30s in the 920s), and you'd be able to purchase 6 whole ploughteams of oxen, which could make you a fairly comfortable living. In terms of land and tenants, either sum is theoretically enough to enable you to live comfortably as a Freeman farmer or maybe even to join the lower ranks of the nobility, period depending. According to Wulfstan in the early 11th Century, ownership of 5 hides of land qualifies one as a thegn ordinary, as this assumes responsibility for roughly some 20 villein households, or some 40 smallholders (or a mix thereof, of course), potentially some 100-200 people. The estimated income from a hide of land - roughly analogous to a "ploughland" at Domesday - is very, very approximately about 1L annually, so your 12L 10s is very roughly equal to the annual income for 12 and a half hides, or some 1,500 acres. These are annual incomes, of course, so don't expect to just be able to buy that 12 hides and assume the mantle of a thegn. For reference, a large settlement like Wimborne Minster had a population of some 150 households working some 45 ploughlands with an annual income of around 100 pounds.
A charter of 774 from Tuscany concerning the sale of part of a vinyard between two individuals (ChLA 36:1047) sets the price at 5 solidi, roughly the same as 5 mancuses, or 150d. A 926 charter of Æthelstan (S 396) confirms the ownership of 5 hides of land which his minister Ealdred had previously purchased from the Danes for 10 pounds. Another (S 397) to an Uhtred confirms his ownership of 60 hides in Derbyshire, which he had purchased for only 10 pounds. It's hard to use these to put any concrete value on the price of a hide, however: Uhtred in particular seems to have been a shrewd operator who was able to acquire a substantial estate for a steal, having probably been quite opportunistic in taking advantage of Danes wanting to get any potential profit from land before they were driven off of it by the Mercians. Ealdred's price, of two pounds for a hide, is a bit more likely, but again he was probably able to capitalise on there being some Danes very eager to sell.
It's worth remembering as well that agriculture operated on a three field crop rotation system, so to get the income from 2 hides, you'd want to actually own 3.
Not really. While you're wealthy to have a purseful of gold (though silver is the coin of the realm) and unlikely to be considered a mere peasant (though without a good story of recompense for noble deeds you might be considered a rogue), you can't strictly buy land or the seigneurial rights that come with it: they have to be granted to you subject to your ongoing fulfilment of associated service to the lord who remains your lord - and even he's similarly obligated all the way up to the king.
You could perhaps pay someone to grant you the land and the rights that come with it, but you're still still not technically the owner and you remain subject to expropriation if you default on your obligations (which you can't just buy your way out of, because they're subject to custom rather than the market - their incidence can be adjusted, but that too will presumably cost you under this shady arrangement as the lord still owes the same obligations as before to whoever's above him in the pecking-order). So "ownership" (least of all of those desirable seigneurial revenues) isn't outright in the sense of a modern freehold market unless perhaps you're the ruler - and even his rights as monarch only exist so long as he wears the crown.
What you can do in the 12th century is rent an estate, paying the lord a regular amount but living off whatever else you make out of it and the tenants who come with it. Though the lord is doing what we'd call the farming-out, you're the "farmer" of this "farm", hence our term. You're still not the person with the nominal entitlement to the associated peasant obligations, but the profits are yours for the duration of the arrangement, which seems to have flourished until 13th-century inflation made it more gainful for lords to exploit the land directly.
Are there better opportunities in town? Perhaps, if you're shrewd: you'll still owe a rent to the titular holder of the property and taxes to the appropriate authorities, but otherwise you're free to profit through subdivision and sub-letting. It's hard to say which is the more profitable arrangement as the absence of commercial "ownership" and sale of rural land means there's no way of valuing it, but by the time we get to modern asset markets urban housing is a more lucrative investment than land, as it has tended to remain: for the best of both worlds, it pays to profit in town and do your spending elsewhere.
Well if we use this currency converter from the national archives, https://www.nationalarchives.gov.uk/currency-converter/#currency-result
Set to 1300 and assuming 100 pounds, that's approximately £70,902.98.
Which is calculated to be worth approximately 117 horses or 10,000 days wages for skilled labourers.
Being able to afford food, horses and labourers would definitely put you in a good position. Land is a trickier thing because it depends greatly on the individual value of the land in question. Some estates were worth more than others. Certainly at least, the ability to afford a good amount of wool (434 stones if you spend all of it on that) could set you up in trade and you could earn a larger income that would go towards setting up an estate.
However, of course as you allude to birth was a huge part of European society around this time. Not only whether you had a title, but how old the title was, how senior a title it was, what kind of reputation your ancestors had, if you weren't a noble how many of your ancestors at least owned land, knighthoods, parliament?
If you are a modern individual, it is unlikely you have such a pedigree and even harder to prove it if you do. Early Modern example, but William Cecil, 1st Baron Burghley became the most powerful man in England during Elizabeth I's reign as her no. 2 but the Cecils were of obscure Welsh origins who had only achieved (minor) significance since Henry VII, before Burghley skyrocketed them. In later years after he obtained a title, he became almost obsessed with heraldry and genealogy attempting to brush up or even fabricate a better ancestry. Even when people became a new lord, it didn't stop the resentment of those who knew where they came from. The irony is that many of those lords that sneered at rising gentry in the Late Medieval and Early Modern Period had come from somewhat similar origins, they just had more generations between them. The new thing was the increase over time in creations for those without noble blood and the particular merchant/lawyer/bureaucrat class many came from whereas older lineages were more likely to have been knights.
So, in your position climbing the ladder throughout capital you would definitely engender jealously and suspicion from established nobles, through that doesn't prevent you getting quite far with the right circumstances. For a Medieval example Michael de la Pole, 1st Earl of Suffolk's father was a wool merchant but he became Lord Chancellor in 1383 and an Earl in 1385 due to royal favour like Burghley.