Is there a recommended class to play in this game?
Good answers so far already, I will just add that a pure melee fighter is also very easy. So easy, in fact, that you can spare time for investing in either magick or technology as well, to make things more interesting.
Having said that, even the "hard" characters aren't too hard, i.e. it's definitely possible to play a sub-optimal character and still have a great time. Arcanum is really good at rewarding differetn play styles and different roleplaying decisions. So don't be afraid to try something crazy. For your very first character, however, you may want to avoid guns and instead focus on a magick user, a melee fighter, or a throwing specialist to have an easier time.
Are items dropped or in chests random or the same each time the game is played? Is there much grinding involved?
I think it's a mix of both. There are definitely places with fixed loot, where you can always find certain items. But I think many other instances are randomized.
Is there much grinding involved?
Not really. There's one location reasonably early in the game that's something of a difficulty spike if you don't know what to expect, but if you spend time exploring and doing side quests first, you should be able to tackle it without doing any true grinding. Having said that, it's certainly possible to grind by simply exploring the wilderness and fighting random battles.
Some of these advantages/drawbacks are on purpose, to highlight the differences between the setting's old-school magic and the far newer technology. But some of it is because the game was rushed to market right before Troika folded.
Arcanum was rushed to release, but it wasn't because Troika folded. Arcanum arrived in 2001, but Troika went on to release The Temple of Elemental Evil in 2003 and Vampire: The Masquerade -- Bloodlines in 2004 before folding.