I've played this game a bit over the years, here's my ranking for ascension difficulty for each class:
Warrior - Medium, highly dependent on gear for damage output. Can be built in many different ways, although its safer to use mana for supportive spells instead of attack spells. Pure melee builds tend to struggle against ranged enemies in open areas and rely on Charge and Deflect. You'll often have to wait around corners to Power Strike ranged enemies that peek. Deflect is risky to rely on against high damage shots from lava eels etc but can be sold when combined with a shield or ring of reflection.
Barbarian - Hard, lack of mana bar and reliance on rage for ability cooldowns makes Barb completely dependent on melee and ranged weapon drops, 99% of the time you're gonna want a full melee focused build unless you find a good ranged weapon early on, and even then investing heavily into ranged just makes you an inferior Ranger. Rage gives you a bonus to ability cooldowns when getting kills, as well as bonus melee power. A properly built up Barb can mow down hordes of enemies with strafe attack and rage bonuses but tends to rely on wands, scrolls and charms to deal with tower enemies. Also, the rage mechanic means Barb is unable to fire off a Power Strike then retreat to the upstairs and wait for the recharge, meaning that he can get "stuck" if the next floor is swarming with enemies that he can't take on in one go.
Rogue - Easy, maxing stealth and dex enables Rogue to walk up and slay enemies without them realizing, high stealth crit multipliers can give you 200+ damage on a single hit with a decent melee weapon. Sleeping Dart is your most valuable skill and lets you instantly kill anyone who detects you. You probably can leave it at level 1 though, since there's rarely a reason to leave enemies sleeping for longer. When facing swarms of enemies just stand on the upstairs and drag up anyone near you. You can use smoke bomb to obscure vision and force ranged units to walk into melee range before dragging them upstairs. High dex investment also makes Rogue a decent ranged attacker that can one shot any medium health enemy that crosses water.
Ranger - Easy, each skill Ranger starts with is strong and you'll wants to invest in each eventually. Probably tied with Enchanter and Necromancer for strongest class. A Ranger with strafe attack an a longbow will pick of hordes before they can get close, Power Shot lets you snipe high health enemies, and Tunnel Shot clears corridors. A high level ranger will have the tankiness of a Warrior (assuming you reach max evasion) and massive ranged damage output. Your high dex will also give you massive crits. Just be careful when in the final levels, as your Tunnel Shot can reflect off a crystal golem and kill you.
Fire Mage - Medium, Fire Mage hits hard but is squishy like most mages. Their most useful spell is the basic Fireball, which allows you to hit one tile further due to its blast radius. Burst of flame is useful for high health enemies and towers, but otherwise you won't often make use of its area effect version. The other spells are ok but Flaming Hands is useless, I have no idea why it's in the game as your basic fire staff will deal more damage.
Storm Mage - Medium, their power heavily depends on positioning of enemies, themselves, and any water sources. Shock is their strongest skill and allows you to instantly clear any monster rooms you open. Just be careful of zapping yourself to death, investing in Levitation if you have mana to spare allows you to fight enemies while over water.
Ice Mage - Hard, the range of their Cone of Cold spell is pitiful and their best spell is Freezing Cloud. For most difficult encounters you'll want to lay down a cloud of two while backing up, then use your staff to pick off any stragglers. Reserve Cone of Cold for single enemies or anyone invading your personal space. Ice Armor is an ok buff, but only useful if you have the mana to spare.
Necromancer - Easy, the extreme range of the Life Spike skill combined with health to mana conversion of Cannibalise ensure that you will always a decent chunk of mana and health as long as enemies are around. Even on its own, a Life Spike lets you fire and forget to eliminate high health enemies, while healing yourself, and all from the range of a bow. Infectious Disease is useless and likely to kill yourself, and I found Skeletons to be quite mediocre and only useful if you absolutely needed a meatshield. Once your Life Spike is powerful enough you may want to invest some points into increasing your health, cause more health means more mana, and vice versa. A Necromancer juggling a strong Life Spike and Cannibalise may only need to eat a couple times throughout the whole game.
Enchanter - Easy, the effect radius of Confusion grows whenever you upgrade it, so max it out as early as possible. Casting confusion then retreating can clear out any monster horde. Swiftness is a powerful buff, so make sure to pump your mana high enough to sustain it. Their one difficulty is dealing with lone monsters. If built as a full caster, you can string them along with Charm until you run into another bunch of monsters. A fun build with this class is investing into dex and stealth, as Mesmerize works as an AOE version of Sleeping Dart, and a leveled up Confusion is still very powerful without any investment into spell power.
Note that these are general guidelines for a new player, you can pretty much build any class into a melee brawler, melee stealth, ranged, or caster (except Barbarian) build, depending on the gear and skill books you find.