The main things I look at for a good host are the time in business, at least one year, but more always helps, I need to know they'll be around.
Next is their uptime, I need my sites to have great uptime.
Another is the price to plan ratio. I want a good amount of space and bandwidth. If its too low, I won't even consider the host, and if its too high, like 10 gigs of space and 500 gigs of bandwidth for like $7.95, I leave, that is WAY to much overselling.
Next is reviews, if the hosting company has been around for a year or more, it should have some good or negative reviews somewhere.
As for support, I'd of course like good support, and a fast response, within an hour or two, but that doesn't really effect my decision. I'd rather have a host with great uptime, reliability, and great packages and decent support, then a company with decent uptime, reliability, decent packages and amazing support.
As for the company owning datacenters, or their own server, that helps a bit.
But I think I guy on a reseller account, with a good business plan, might be a better host then a guy who rents a dedicated server, who's too say the dedicated server guy won't be able to handle the high monthly server costs, and your site goes down, while the reseller guy can handle the lower payments, and upgrade to a server when he has the customers and income too.