For example... lets say crazycat.com was available... and crazy cat was searched for 300 times a month according to overture... would you pick up the domain? or would you prefer something with way more searches? note: I know domain name isn't everything when it comes to SEO, but it still plays a role
Depends on a few factors. How commercial the keyword is. How hard it would be to rank for the term. I usually would want at least 2000 OVT.
what if there were only 1500 searches per month, but it was for a really high paying adsense keyword?
Again, it depends on the competitiveness of the term. The CPC is meaningless if you can't generate traffic.
What is the best way to check the competitiveness? allinanchor:"keyword" allintitle:"keyword" ? anything else i can do?
Depends on the niche, keyword, etc. If it's your brand... than it's worth it even if there is no traffic for this keyword