There are a lot of great places to buy comics online. The internet has a lot of stuff. First of all, I genuinely think nothing beats going to an actual comic shop. I am sure you know if you live near one, but in case you don’t you should use www.comicshoplocator.com to see if there are any shops near you.
After that I am partial to Forbidden Planet (www.FPNYC.com) because that is my local comic shop and I write a column for their blog/newsletter. If you are looking to get subscriptions to regular single issues people always say good things about Discount Comic Book Service (www.dcbservice.com). I have never used them because I live in a big city with lots of local shops though. The other heavyweights of comic mail ordering are www.Midtowncomics.com, www.TFAW.com, and www.GrahamCrackers.com.
If you just want to forgo having physical books (which you shouldn’t, physical books are awesome), you can get most of the major stuff from www.Comixology.com. If you do buy stuff from Comixology please remember to buy it from their website not their app as it makes much more money for creators and publishers that way.
Also keep in mind that some cool publishers out there do mailorder for their books. It helps them out a lot to buy direct. Hope that helps.