This is not related to search engine optimization but will affect on how your site will stand to the millions of visitors on your site. For example is the graphics being displayed? That means GD should be enabled. Thus security is enough to protect your site? DO they allow or do database back-up in case of problems encountered by your site?

Typical question but will affect primarily how it can kill your site agenda and loose the visitors you want.  Here some basic information (at least for me though not technical) that can help you choosing the right web host for you.

1. Check how long they have been in business. But I am not necessarily being there for a long period already means they are the best or just been put up they are not. Next tips will show you why.

2. Does your site or the script you are using needs graphics function like GD and others like mod_rewrite?

3. Check the php version, sql, or any other software that comes on the host.

4. Check where it is located. Most asia located server are offered at the high bandwidth. Why? most of the time they are measured on the resources consumed.

5. Make sure your host is not blocking search engine spiders to indexed your site.

6. Check if your web host is indexed.

7.  Check other websites hosted on your web host. This is the one I always check into.

The tip number 7 can give you a hint if your site will be likely down frequently or not especially for shared servers. Check whether your host (where your site is) is accepting sites like porn, gambling or high yield investment programs. You should be thinking already that this sites is a frequent target of attack, malicious codes, DDoS and other attact compromising all sites hosted on the same server.

Well this is just my opinion and it is up to you to decide.