The Radeon 7750 1gb GDDR5 PCIE 3.0 does not use any external power from the PSU. It draws all it's power through the PCIE bus on the motherboard.
PCIE is backwards compatible, meaning that the newest 3.0 video cards will work on any PCIE slot all the down to 1.0 and anything in between.
As far as your PSU is concerned, I always tell people that having a quality PSU is the most important component in any computer. The generic PSU's that most "store shelf" computers come with provide just enough power to keep the systems running.
Having said that, can you upgrade to a 7750 without upgrading your PSU? Yes you can as it won't draw any extra power. Should you upgrade your PSU to protect your investment? Yes you should.
I don't understand the question about the motherboard.
As far as a PSU goes, it really depends on your budget. The Corsair CX430 is a decent, low end PSU that is highly recommended. It was just on sale for $38 ($18 after rebate) but is now $50 ($30 after rebate). A better PSU (for the same price) would be the FSP (Fortron) Raider 450W It's also $50 ($30 after rebate).
Unfortunately, even with it being "Cyber Monday" I'm not finding very good deals on PSU's.
Edit: One thing to remember, and this is all based on your budget, if you upgrade your PSU you will no longer be constrained to the 7750. With a quality 450W PSU you would be able to run a Radeon 7770 / 7850 / 7870 without any problems. Anything higher would need a PSU with a higher output.