I would second Amazon Web Services but I believe the free instance is only good for a year (my free time ended after a year for a micro-instance). Although many here would suggest GoogleAppEngine I avoid Google products for business critical anything just because I have found their support to be very poor or non-existent.
For a domain registrar I have used Register.com (avoid like the plague), GoDaddy and most recently transferred a couple dozen domains to NameSilo (http://www.namesilo.com/). I had used GoDaddy for years when they were among the cheapest but since their private equity buyout and IPO they have eliminated all their discounts for existing customers and renewals which makes their pricing uncompetitive. NameSilo has great pricing (among the lowest based on my research), they have a good system and clean interface/dashboard, I completed the transfers from GoDaddy to NameSilo within an hour by following their instructions exactly and so far have been very happy with their service. I considered NameCheap which a lot of HNers seem to use but NameCheap doesn't offer any live phone support only email and chat which was a complete non-starter for me. I had a few questions about NameSilo's services and pricing and made a couple of calls their support line which were answered by a live human with no wait and they knew their stuff and answered what I needed. It is a great value with their registrar systems/services, pricing and live phone support.
I still have some domain names with GoDaddy but as soon as they come up for renewal I will transfer them to NameSilo and I will be glad to not have to deal with GoDaddy' frustrating support people who just want to sell you crap as well as not missing the non-stop barrage of promotional crap they send to you which before they eliminated their discount coupons you had to receive in order to get their no longer available discounts.
For a domain registrar I have used Register.com (avoid like the plague), GoDaddy and most recently transferred a couple dozen domains to NameSilo (http://www.namesilo.com/). I had used GoDaddy for years when they were among the cheapest but since their private equity buyout and IPO they have eliminated all their discounts for existing customers and renewals which makes their pricing uncompetitive. NameSilo has great pricing (among the lowest based on my research), they have a good system and clean interface/dashboard, I completed the transfers from GoDaddy to NameSilo within an hour by following their instructions exactly and so far have been very happy with their service. I considered NameCheap which a lot of HNers seem to use but NameCheap doesn't offer any live phone support only email and chat which was a complete non-starter for me. I had a few questions about NameSilo's services and pricing and made a couple of calls their support line which were answered by a live human with no wait and they knew their stuff and answered what I needed. It is a great value with their registrar systems/services, pricing and live phone support.
I still have some domain names with GoDaddy but as soon as they come up for renewal I will transfer them to NameSilo and I will be glad to not have to deal with GoDaddy' frustrating support people who just want to sell you crap as well as not missing the non-stop barrage of promotional crap they send to you which before they eliminated their discount coupons you had to receive in order to get their no longer available discounts.
Good luck to you...