Which is the best domain & hosting company?  

try this

http://www.snoobhosting.n...

Opinion posted here will be subjective. It will vary from person to person. You can find some people recommending godaddy, hostgator and bluehost. Some people will even recommend dreamhost. Some will recommend some another hosting company. If you're looking for linux based hosting server then most of them are cheap and reliable. You can choose hostgator, dreamhost and bluehost in this case.

For alertpay i'm not sure,if any supports it. But many hosting companies support paypal,liberty reserve. You've to contact alertpay services to ask them about such merchants.

hey i don't know about more sites....but i have hosted my site with quick2host.com....they are really good...and i never got any problem from them..and also the rates are very cheap....so you can try this one if you wanted to hosting some site.

Hey actually you are asking two different questions. Major players in both the niche are different.
For domains - Undoubtedly www.godaddy.com
They give you some freebies (like facebook credits) also
For Paid hosting - Hostgator.com
For free hosting - freebeehosting.com (Though they provide paid options also)
I am getting my site www.justawebmaster.com hosted freely on freebeehosting.com. Its superb and I never faced any problem.