Personally I'd go with Sentinel or Adept. I love ME1, but gameplay wise there are some advantages you can exploit with Adept or Sentinel that break the game on higher levels when you start to get shorter cool down times and can actually withstand a fair amount of damage (even on Insanity). I've played soldier class and vanguard as well and they were enjoyable too, but I've not had as much fun as I have with Adept and Sentinel on high levels.

I've never found the weapons to make a huge difference in terms of how I play the game. Shotguns require you to play at shorter range, but pistols and assault rifles were never that different IMO. So limiting yourself to a class that can't use assault rifles is pretty meaningless. As a Sentinel you can raise your electronics and decryption skills to the point where you don't need someone else with tech to be on your team which gives you a lot of flexibility in how you structure your team on missions. Then you are free to focus on maxing out biotic skills. Lift, Warp, Stasis, and Throw were always what I focused on as a Sentinel outside of Electronics and Decryption. Those biotic skills always made the game a cake walk when you get to higher levels.

Around level 20 some things happen that really turn the game into a ton of fun for Sentinel and Adepts.

(SPOILER) The moon mission gives you the opportunity to specialize your sub class, and I believe the Bastion option as a Sentinel allows you to deal damage to enemies in Stasis. So a maxed out Bastion and Stasis, along with maxed warp, lift, and throw really break the game IMO. Especially at later levels when cool down times decrease substantially

Adept is similar, you just lose the ability to have the electronics and decryption skills yourself and have to include Garrus, Tali, or Kaidan with you to gather loot. Adept also gives you singularity which is completely worth it from a crowd control/game breaking standpoint. Barrier is also a necessity to help you withstand damage. At later levels you are pretty fireproof if you spec your armor right as well. Not quite to the invincibility that comes with a Solider who has Immunity, but damn good.