Question about swapping parts from one pc to another.

1) Thats a pretty tight budget for a good PSU. Generally look at Seasonic and XFX series for the solid top tier models. Corsair has some good models, but those models are very specific (and are typically built by Seasonic). If you want to modular its going to jump the pricing up a bit. I'd look for semi modular, it'll at least reduce the clutter but be less costly than a full modular PSU. I'd recommend upping your price budget for the PSU if you can, its one of the most important parts of your build. Manufactures always have some sort of deal going for rebates or sales on an item. For more than you ever wanted to know about Power Supply Units, give these a read. It should help you decide where you want to go.
http://www.tomshardware.com/forum/id-1804779/power-supply-unit-tier-list.html
http://www.tomshardware.com/reviews/power-supply-psu-brands,3762.html

2)There are a bunch of different opinions and products out there, but most shops and people I know personally just use rubbing alcohol and cotton pads to clean the materials. Don't drench the anything in it, but a little on the pads and wiping the compound away will work. Make sure to give the CPU/heatsink time to fully dry before reapplying. Of course be careful to only touch the lid of the CPU and the base of the Heatsink/fan. Also if your using a copper heatsink double check what you do use so you don't corrode anything. For more than you ever wanted to know about thermal compound check these out.
http://www.tomshardware.com/reviews/thermal-paste-heat-sink-heat-spreader,3600.html
http://www.tomshardware.com/reviews/thermal-paste-performance-benchmark,3616.html

3) If you're really concerned about static shock, look in to proper static handling procedures. Pick up a static mat and wrist strap. That being said, not many people bother with this step and get by. As long as your not working in wool socks on a carpet while its super dry out, you'll likely be ok. Just avoid touching the PCB of anything you build and touch the metal framework of your case/psu to discharge anything you might have built up before touching a component. As for once you have the computer built, don't worry about putting the new build on the carpet. That's one of the reasons a case is there in the first place. You're more in danger of carpet fibers, dust and animal dander clogging up your computer and setting it on fire than you are zapping your computer because its sitting on carpet.

OK so for the PSU, that should be fine. You're looking at a good upper middle to lower top end with that model. Without knowing your exact system specs I'm guessing you're roughly in the 400watt range of actual usage. However your card calls for a min 600watt supply according to Nvidia. Manufacture specs always over estimate actual needs so a 650watt should be fine to keep everything running smooth. But if you ever intend to SLI the card it wont be enough. So just food for thought on future expansions.

For the thermal compound, that should be fine. Its as good as roughly 80% of the ones out there and its inexpensive, just make sure you apply it correctly when you reapply. However you may want to consider a better cooler than the stock intel cooler. To be honest they suck. They work, but there is a lot out there thats better for not very much. The new case your looking at affords CPU coolers of up to 170mm, so I'd recommend looking at something like the Cooler Master Hyper 212 EVO. Runs about $35 US and will out perform the stock cooler.