First of all the evaluation of Waffen SS division is often emotionally and rarely objective. Waffen SS units more than other combat units in the European theatre were responsible for war crimes. From the very beginning of WW2 Waffen SS divisions were tied to warcrimes. Over the war nearly all major divisions were involved in such war crimes. Those war crimes included indiscriminate killing of POWs and killing of civilians. While the majority of war crimes happened on the eastern front they also happened on the Western Front ( Normandy Italy). In Normandy for example nearly all major war crimes were committed by Waffen SS units. Whatever legacy they might have earned in combat it is undoubtedly ruined by their ruthless criminal behaviour outside of combat.

To your questions. Some general remarks which will demonstrate the difficulty with answering your questions.

Waffen SS divisions varied highly in performance this was mostly due to their intended purposes. Many later divisions were never intended as elite divisions or even for frontline duty let alone offensive operations. In contrast to the Western Allies not all divisions were raised equally. A Panzerdivisions raised for offensive operations was equiped differently to a unit intended for other purposes. Not only in terms of tanks but also in terms of trucks and other equipment. 38 divisions were raised and only a handful of those can be considered elite . Another problem with such questions is that the war lasted for 6 years and things changed. The 1st SS Leibstandarte Adolf Hitler was only a infatry regiment ( mot) during Polish campaign but in Summer 1943 it was one of strongest Panzerdivisions in the Wehrmacht with their own Tiger unit.

I will focus my answer on the units generally considered "elite". This would include the 1st LSSAH, 2nd Das Reich, 3rd Totenkopf, 5th Wiking and the 12th Hitlerjugend. The 9th and 10th could also be included maybe.

To your questions.

Were they given the best material or men?

For the mentioned divisions yes. But this changed over the course of the war, most Waffen SS units were not divisional size in the early war but were reinforced regiments or smaller. But after the early campaigns those units were upgraded to full fledged Panzer divisions they got very good equipment. A good example for this would be the II SS Corps during Kursk. After the outstanding performance of the three SS divisions during early 1943 they were upgraded and even got their own Tiger companies. Over the course of the war, only 4 divisions got their own organic Tiger unit. 3 of those were SS divisions the other one was the Großdeutschland division. This speaks volumes to the equipment question.

The 12th SS Htleryouth for example was raised with the "best" young men from the Hitleryouth.

After 1943 the prime Waffen SS divisions kept being supplied with plenty equipment. An example for this would be the 12th SS which in Normandy was the second strongest Panzerdivision only behind the "prestigious" Panzerlehr. Equipped with a full Panther battalion and good mobilization with SD.KFZ 251s it was one of the best equiped units opposing the Allies. It was also the biggest units in terms of manpower followed by another SS unit the LSSAH. Of the 4 strongest divisions 3 were Waffen SS. This trend was continued with 6th Panzer army getting the focus in the Ardennen offensive. The 12th and 1st SS were the strongest units in terms of manpower during the Battle of the Bulge. In terms of tanks the LSSAH was the strongest German unit engaged in the Bulge even getting a full strength King Tiger battalion attached. The 12th SS was second strongest if assault guns are included. A clear trend to focus on the Waffen SS units. Later in 1945 Waffen SS units were chosen for the last major offensive towards the East ( Operation Spring awakening). The prime Waffen SS divisions were supplied with the best tanks possible for most of the late war often being the only units full equiped with a Panther and Panzer IV battalion.

Did they maybe receive "Prestige missions"

From 1943 they were chosen for the center of attacks. In Kursk the II Panzer Corps was the strongest corps and the center of the southern wing. During Normandy the SS unit were intended to lead the counter attack against the beachhead. In the Bulge the 6th SS Panzer Army was the center of the attack. Spring awakening was mostly SS units.

Was there much range in effectiveness within the SS?

Extreme ranges. Some of them were without a doubt the strongest divisions during WW2 some of them were only intented to control occupied territories and fight partisans.

About performance.

This is a difficult topic and you will find evidence to support both sides of the argument but overall the mentioned divisions performed very well, especially from 1943 onwards. Dissecting every battle is to much for this topic but to name a few outstanding performances:

Third Battle of Kharkov:

Considered the biggest german victory in 1943. A far bigger soviet force was mauled and the frontline was restored which was the prelude to Zitadelle. This was achieved on the back of the II SS Panzercorps which were the first three Waffen SS divisions. The soviet casualties were very high in terms of man and material. The performance here played part in the decision to upgrade those units and use them as spearhead against Kursk.

Battle of Kursk:

The three Waffen SS divisions achieved the biggest break in and were responsible for massiv soviet casualties which culminated in the battle of Prokorovka which was the biggest single day tank battle and resulted in tactical showcase for Waffen SS performance. Hundreds of soviet tanks were lost for a handful German casualties.

Following Kursk:

After Kursk the Panzercorps was broken up and parts of the SS units helped repel the Mius attack and later destroyed vast amounts of tanks during the Belgorod-Kharkov offensive.

Normandy:

The 12th SS is considered one of, if not the, best performing units in this campaign. The unit inflicted loop sided casualties on the Allied attackers of the entire campaign. Never letting a significant breakthrough occur against very loopsided odds.

Market Garden:

The main defending defense force were two SS divisions. The performance is considered good as far as i know but iam no expert for this battle.

Battle of Bulge:

The SS units performed very poorly here. It's hard to pinpoint the reasons for the failure here but especially for the 12th SS it has to be said that the major advantage for the Normandy campaign, long preparation, was lost here. The unit was more or less bled white in Normandy with mostly trail surviving from now on the unit sufferered from the same problems as other units, very short basic training.

While the following is not really proof it gives you a good idea about combat performance. Of the top 5 divisions in terms of Knights Crosses, 3 are Waffen SS despite the fact that most Waffen SS units were only upgraded to full divisions in 1943.

Another indicator:

The 2nd SS Das Reich is the unit with the highest tank claims and likely the unit which destroyed the most AFCs in history. I don't see a reason to expect the unit to overclaim more than other units. This unit also leads the list for Knights Crosses. This all despite joining the combat rather late. This indicates the unit was chosen for many heavy battles and performed well. Other units high in this list fought already in Poland.

There was a very nice answer last year from /u/kronpas that addressed variability in SS effectiveness at https://www.reddit.com/r/AskHistorians/comments/23r7iq/what_was_the_difference_between_the_nazi/

Of course there is always more room for commentary.

To complement the big post, some of the Waffen-SS divisions had very specific assignments in how they were made up - for example, 7th and 13th (Prinz Eugen and Handschar respectively) Divisions were classed as gebirgsjager, or mountain infantry - very few vehicles and even lighter on armour, though usually generously equipped with lightweight heavy weapons. 8th SS "Florian Geyer" was a traditional horse cavalry division, equipped accordingly, though with some motorised elements.

The bulk of the first dozen or so divisions were, as u/ChristianMunich posted, the "elite" units, often at full strength, both in manpower and equipment allocations, and also as posted, more so later in the war - LSSAH was the longest serving formation (1933 onwards), while 2nd through 6th became operational between 1939 and 1942. Others of the "elite" divisions were formed later in the war - a notable example being 12th SS "Hitlerjugend" being formed from cadre supplied by 1st LSSAH and enlisted volunteers who, while over the age of 18, had mostly been members of the Hitler Youth as children.

Most of the rest were regional ethnic units formed as anti-partisan forces, and almost universally divisions in name only. One notable exception was SS-Division Dirlewanger (listed as 36th Division of 38), and was for the most part, a penal unit. When we say the Waffen-SS committed the lion's share of war crimes, it's not an exaggeration to say that Dirlewanger was particularly brutal, even allowing for its small size.