I don't know what to tell you...I mean, if you liked Hitman and Thief, I don't know why Deus Ex would rub you the wrong way.
Anyway, as for some tips...make sure you invest in your Computer and Handgun skills early on. One level in the former will allow you to hack into all computers, security terminals, and ATMs, which can get you all sorts of good stuff if you work fast. As for Handgun, the regular pistol can be pretty powerful if you upgrade it and given a scope and ammo for it is common for the first half of the game.
You will eventually want to invest in another type of weapon too; between Rifles, Heavy Weapons, and Melee, pick one and stick with it. I find Rifles are the best all-around and are great for a beginner (the Sniper Rifle is godly), but it's up to you.
Invest fully in either Lockpicking or Electronics. There's no need to pick both. A lot of doors can be opened with both lockpicks and multitools and combined with hacking and a few spare explosives, you shouldn't really have any trouble getting past locked doors.
Explore, explore, explore. You can get a surprising amount of skill points this way and you can never have too many.
At the beginning of the game, when Paul gives you a choice of three weapons to take, take the GEP gun. You can get the other two weapons can be found on the first mission, but it'll be a while before another GEP surfaces. Even at low Heavy Weapon levels, it can be pretty handy at taking out bots from long range thanks to its lock-on capabilities, and it can make a handy "lockpick," heh, heh, heh.
Play stealthily at the beginning. Your aim svcks at this point and you have no defensive augs, so take it slow. Take some time for your reticule to narrow down when you plan to shoot bad guys dead, and be prepared to hide if too many guys see you. If there are any allies in the area, feel free to lure your enemies straight to them. Don't be afraid to try and sneak up on enemies and take them out with a melee weapon to the head; you can knock them out silently that way.