Based off your list, here are my opinions/experineces with the heroes. Ones I bold are ones I own play, so its first hand experience, others are experience from playing against.
Graves-Deceptively tanky. Shorter range than your typical carry, but also does more up front damage, especially at level 6. Can definitely capitalize on kills from the burst early to snowball later.
-Urgot-Not as difficult to play as people make him out to be. Land your E (poison) and you inflict serious pain on your opponents with long distance Q direct hits. Not the strongest pick bottom--you'll need a good friend to help with kills against sustain heavy lanes. In the right situations he's awesome either top or mid against champions that are solo without tons of sustain.
-Twisted Fate-Can be AD or AP type build, but generally see him as AP these days, I find. His ultimate is great at securing kills by making once teamfights your opponent thinks are even lopsided.
-Vayne-Need to use her condemn effectively to shine early. Good counterpick to tanky teams
-Tristana-Generally solid Ad carry, her jump is one of the better escape abilities. You aren't going to be doing tons of burst damage early. Can farm a lane well (even too well if you end up pushing too far) because of her ability that makes creeps explode on death.
-Vladimir-Not your standard AP carry. Vlad lacks a strong crowd control ability and does the most (AOE) damage when he's in the fray. He does not do a lot of burst early. However, when he gets a few levels on his Q and a hextech revolver, he has insane sustain, and his pool ability makes him hard to kill.
-Brand-Combo based AP caster. If you can hit his skillshots, this guy is awesome. Has a long range so he can sit back and use his abilities pretty comfortably, which makes up for the fact that his one stun requires you to land a couple of abilities.
-Morgana-If you can't farm with Morgana, there's no hope for you. Honestly when you're trying to learn to last hit, it's probably a bad idea to play Morgana cause she can farm so effectively with tormented soil. Her passive gives her free spell vamp, which again combined with soil gives her good sustain in lane. Her shield is really powerful to avoiding getting CC'd (and killed). She's great top or mid solo, and can sort of be a support (not the best pick). Learn to combo her abilities well and you'll see why she's banned.
For specific build info, go to solomid.net. Look at featured and approved guides to see what skill order and items to use, etc.