It's hard to give you an advice about Deus Ex 2 because it's one of these love-it-or-hate-it games. I loved it (even if I have a few complaints), a lot of people hated it. I think the best way to sum it up is: more FPS, less 'RPG'. Some say the best way to enjoy it is to forget the first one, and play it as a new game instead of a sequel.
It's not a First Person RPG with stats and inventory management. It's a FPS with RPG elements. You don't have stats, and the only impact you'll have on your character will be the choice of his 5 bio-modifications (with 3 different possibilities for each slot). The inventory management is also a lot simpler. On the other hand, the action part is also much more action oriented, which I enjoyed (especially when I tried getting back to the first one afterwards).
Max Payne 1&2 are really good. Great storytelling, great gameplay, some excellents mods (especially Katana for Max Payne 1)... Really worth getting, especially considering the price.
About games close to Shadowrun, that depends on what aspect of Shadowrun you'd like to see. Here is my own list (minus what's already been mentioned). As I don't play a lot of recent games (and considering that a lot of the cyberpunk games are quite old), it includes a lot of old games. They can probably be downloaded on abandonware websites if you can't find them anywhere else.
Cyberpunk games* The Genesis and SNES Shadowrun games, of course. The Mega CD one looks really great and faithful to the PnP game (down to the management of dice pools and rolls being shown on screen with associated TNs) but it's only in Japanese and no translation has yet been released.
* Blade Runner: a really nice adventure game based on the movie. The story is different yet very close to the movie's, you get to visit a lot of familar places and even use the Voigt-Kampf test.
* Bloodnet: very probably Shadowrun-inspired (I mean, they mention Ares guns here and there). Set in a 80's cyberpunk world (with neo-anarchists fighting the evil megacorp), you play a shadowrunner whose last Johnson happened to be a vampire. You start the game right after having been bitten with your cranial implant doing its best to slow down the vampire transformation. The game itself is some kind of point and click mixed with and RPG. The story is nice and the dialogs are quite good but the combat scenes and graphics (especially the perspective, which makes Arsenal's cover look normal) are a bit awkard.
* Bureau 13: I played this one a long time ago, so I don't really remember everything, but it's a point and click in a cyberpunk with magic setting.
* Burn-Cycle: A FMV (Full Motion Video) game, inspired by Johnny Mnemonic (the story is a rip-off to be exact). It was a great game, but with today's standard it looks quite awful.
* Chaos Overlord: A strategy game where you're some mob boss fighting others to control a city in a cyberpunk setting. The colorful and wicked gangs you hire (wanabees so useless they'll work for free, combat nuns, used cars salesmen) make this game a lot of fun.
* Circuit's Edge: Based on the cyberpunk novel
When Gravity Fails by Georges Alec Effinger. Street-level cyberpunk investigation fun in the middle-east.
* DreamWeb: This game is a work of art, 100% pure atmosphere. It's an adventure game set in a gritty, gritty, gritty low-tech (no implants, no drones) cyberpunk world. The graphics (dated but still quite good, in their own way), the music (excellent albeit dated too) and most of all the attention to details bring the universe to life with a violent, gritty and sometimes strange story. I recommend you read the introductory book
"Diary of a (mad?) man" first both for a better understanding of the story and the added atmosphere.
* Dystopia: A Cyberpunk mod for Half-Life 2. I haven't played it, but I heard that it's really good.
* Hell: A Cyberpunk Thriller. A point and click set in a cyberpunk universe where a portal to hell appeared in the middle of Washington. You play the role of two agents of the fundamentalist government, suddenly hunted by their own employer. The graphics are quite awful but the dialogs are quite good.
* Johnny Mnemonic: A FMV game with a story closer to the one of the movie. The action scenes are ok, but the rest is quite awful, the Matrix scenes being the worst. The gameplay can also be confusing at first. I won't recommend it.
* Neuromancer: Based on the novel. Has aged quite badly and isn't much fun.
* Rise of the Dragon: A very good (albeit short) cyberpunk adventure game.
* Snatcher: A japanese adventure game deeply influenced by Blade Runner. Fun, but much more story-oriented than game-oriented.
* Syndicate and Syndicate Wars: "Corporate Persuasion Through Urban Violence". Two tactical games set in a gritty cyberpunk setting where everyone is equipped with an "Utopia" chip that allows them to see life the way they want. The Syndicates (a mix between megacorps, secret society and criminal syndicate) can control those chips and fight for world domination. You control teams of 4 cyborg agents sent on missions all over the world to lead your syndicate to victory through any means necessary (including Thor Shots).
* Tarmak: A recently released freeware. A retro top-down action RPG set in a classic cyberpunk setting with some magic.
Non Cyberpunk games* Jagged Alliance 1 and 2: A series of squad-based strategy/tactical games where you lead a team of mercenaries. Very good on the tactical angle and full of colorful PCs and NPCs with excellent one-liners.
* J.D Spy: A "puzzle" game that's quite original but very difficult (sometimes feel more like work than game). I think the beginning of the game is a good example: as you play the "start new game" button you have an error message box. Actually it isn't a real error message box, if you click on the "details" button, you see there's a message hidden in the details. Later on, you'll have to learn things about real-life encryption, programming and a lot more if you want to solve the puzzles.
* Kigpin: A violent street-level FPS.
* Operation Flashpoint/Armed Assault: Realistic war FPS. Interesting to get an idea of what war feels like (well I don't know if it's anything like that, but it seems quite realistic).
* Splinter Cell series: A series of Third Person Shooters with a great emphasis on Stealth and Infiltration. Can give a few ideas about infiltration methods or atmopshere.
* Spycraft: A FMV game where you play the role of a CIA agent. Supposedly realistic, it can give a few interesting ideas for Shadowrun.
* SWAT 3/4: Two tactical FPS where you play as a leader of a SWAT team on operations. Really good to see how SWAT teams act and a great inspirations for Shadowrun's HTR teams (or even well-coordinated runner teams).
* Uplink: A hacking simulation with a nice atmosphere. Closer to the real world than to Shadowrun's, but it can still be useful inspiration for hackers/deckers.
Have fun!