Okay, on to basic strategies.
Starting Psylocke (gasp!)
Yes, you can do this. Psylocke is an old-guard pixie, which means if you have a good offense, expect to build oodles of meter for whoever is coming next. A Psylocke who is starting should try to rush down. To do this you have to get their assist out of the way. You can do this by either keeping them in blockstun with an assist of your own (projectile-assist based rushdown), or keeping them zoned with the range of your stand fierce. Once you do that, you can run in with low short or stand jab into a chain (stand strong -> stand forward is best for in close, otherwise just leave out the forward) and end it with one of three things: stand fierce plus assist, stand neutral roundhouse xx psi-flash, or back+roundhouse (hold forward). The first option gives you room to run in again (although if your assist is, say, Sentinel, you probably want to call him early) while the second is good to put a projectile on screen while leaving you safe. The third is a mixup, and should probably be done after doing the second for a bit (since back+roundhouse is basically a hopback regular roundhouse), because it puts you in good place to stick a low short behind them and go into a brief combo.
Speaking of combos, when you start Psylocke, I’d advise you to not go for her aircombo in favor of short ground combos, unless you’re ready to go for a DHC. The reason for this is because aircombos, regardless of what you end it with, leave Psylocke in a really bad position in relation to her opponent. If you do get an aircombo, ending it with fierce will have her up in the air well after the opponent gets up, in a prime position to be crossed up. Generally, you just want to do a chain ending in stand fierce xx psi-flash (won’t combo, but adds to pressure).
Midgame Psylocke
I’m pretty sure that Psylocke would be good in midgame. That’s because she can actually stall like nobody’s business. If you set up a wall of an assist plus repeated fierce psi-flashes from full screen, it’s very hard to approach you. And if they do, you can just respond with short psi-blade, then tap jab jab fierce, fierce psi-flash and repeat the process. This sounds simple, but can get pretty frustrating.
Since the opponent is softened up by this point, you can go for more crossups and overheads. If you have a good assist, you can bait out the opponent’s assist, get next to them, and hit up+roundhouse while calling the assist. This is an instant overhead. If you have A-Storm, you can do up+roundhouse xx short psiblade with Storm assist, and if it connects, you can go for launch to aircombo ending in super. This is SAFE.
Unlike opening Psylocke who rushes down, IMO midgame Psylocke should be stalling. It’s hard to deal with psi-flashes and psi-blade. Don’t give ANY ground here.
Endgame Psylocke
This will happen more often than the above two since Psylocke’s assist is popular. You shouldn’t be afraid to bring her in, especially off of Storm’s AC. If you are winning by a small margin, then stalling is probably the way to go. Otherwise, if you are winning large OR losing, you want to rush. Rushing helps secure your win if you are winning more than running away (although you COULD do that if there are only 10 seconds or less left), and Psylocke’s rush is powerful enough to make some comebacks (watch the videos from 5/25/2002 SHGL tournament videos if you don’t believe me. Jose Garcia’s Psylocke makes comebacks a LOT). I have a thread for endgame Psylocke, though, so I’ll just end it here.