Usually when your PC reboots for no reason and you've troubleshooted all other hardware thats a sign that your PSU is failing. Also the answer to your question is YES
You want the highest rated rails possible, especially the +12v rail, it's hard to find a good PSU with a nice strong +12v Rail.
This thermaltake 560w PSU like I got has a 22a +12v rail, pretty good, I got 10 case fans, 1 CPU fan, 2 in the PSU, OC'd Processor, OC'd RAM, regular graphics card, 2 hard drives, 2 optical drives, and it serves my purposes...if you need more
then there's the Ultra 500w Modular connection PSU which has a +12v rail of 34a!!