Speaking as a player who loves the idea of playing a character which is physically odd:
1. Some of it is 'cool factor'. 'The Most Fragged-up Drake You Never Met,' to file half the serial numbers off a line. The idea of a decker who can get into places without using tech that few people expect. A PC who has to deal with resembling something mythical, or from prehistory.
2. 'What happens if I combine...' Pushing the limits of the numbers and abilities. Which can lead to things like Surged Troll On Skates. Or a quad-wielding pistoleer. Don't ask about the time I tried that with grenades.
3. 'The spam, eggs, and spam ain't got much spam innit.' Ho-hum, another adventuring party comprised of human, dwarf, elf, and halfling. This is a personal reaction to RPGs in general, where it feels to me like everyone is a cookie-cutter collection of stats, while the opposition/'monsters' are vibrant and interesting.
4. 'Look at MEEEEE!' Not sure how much this factors in to my own decisions. I don't like to think that this weighs heavily into my choices of the weird. This is the category of needing to be in the spotlight and stealing the show.
A question that I often see, is "Why would Mr. Johnson even think about hiring Mr./Mrs. Freakshow when there's a million flavors of grey in the Vend-o-Runner?" The player needs to be able to answer that question in spades. And not with, 'well, Jimmy Snowflake is the only one available on short notice.' Jimmy Snow needs to be good at what they do. Really, really good: Nobody expects a creature to fly up to the roof, avoid the drone sensors, and tap into the data lines there. Or yeah, four arms is noticeable, but when the drek starts to fly, they can put down more cover fire than an LMG, without having to try to sneak a fragging machine gun in. Chaps or no chaps.
The one thing that I want to see applied to my oddball characters that rarely happens is the oppression for being different in-character, and the most understandable reason I can see for a GM to deny these options. No mental overhead to feed that line of identical trenchcoat-wearing, bland, sunglasses-indoors Shadowrunners through the missions. The player has their character to run; the GM has the world to run. This is where compromise comes in; having a good story for a character that hooks a GM helps a lot too. 'Glitter here is Incompetent with close combat weapons, especially bladed ones, because she has a nasty scar on one hand from being careless with a big knife. So she's too careful about not hurting herself for using that stuff.' Why did the PC buy that cyber-tail? Where were they when that fragging comet flashed overhead and turned them into... that *thing*.
The other players need to be able to work with that character too; some will shoot an Infected on sight and burn the body, bleach their clothes and check in with their street doc daily. Others won't work with anything weird or unprofessional-looking (though there was that game where the weird one acted professional, and the otherwise-normal guy in a kabuki mask kept stealing the show).
Had to get that off my chest. Though, before you go, Citizen, what's your clearance rating? This is Orange-level information and you seem to be wearing red...
