While I can certainly vouch for the Elementalist as one of the most fun classes out there (and easily one of my personal favorites), I'm not sure I'd recommend it for a first run (well, first as in without the additional items in the vault you can equip them from). As a caster, the Elementalist will need several stats that are hard to find on non-unique items, at least beyond late Normal, I think. You'll need casting speed, you'll need recharge reduction, and most likely you'll want some generic elemental damage increase (if you take only fire, ice or lightning, you might as well go Summoner or Druid). While all of these can be found on non-uniques, they're generally rare and honestly just not good enough.
My first character was an Elementalist; and by that I mean the very first one I actually took seriously. And while it suffered from me not always having an idea of what's the reasonable thing to do, it also suffered from the lack of proper equipment.
Personally, if you want something quick and not very gear-intensive, I'd probably recommend either a melee character (something with Warfare) or an archer (Hunting plus something). Though I'm not sure on the latter, since Scatter Shot Arrows have been severely nerfed in Anniversary Edition. Still, Warfare in melee and Hunting in ranged are probably the fastest you can get, and since non-unique weapons are often as good as uniques when it comes to DPS, they're much easier to outfit.
