Why don't you think about adopting a Standardbred off the track? They often have lovely temperaments. Really most breeds have individuals suited for that but i'd look for a breed that doesn't need too much extra feeding and is suited to your climate. People often give away horses with injuries that can have good temperaments but just aren't suitable anymore.
Honestly, the best thing for your situation may be a Mini. They're awesome little companions & alot of fun. They cost less to feed & you can train them to drive if you don't want to ride ;)
Or like Saskia said, you could adopt a horse in need of a home. Alot of people advertize horses to give away because they've suffered an injury or something in the past and can't be ridden much anymore.
I don't think there's a certain breed that makes a good companion horse. Since you probably don't want to spend a lot of feed (or deal with a hard to keep horse), what about a pony or a miniature? If you are really wanting a horse, pretty much any breed will do. Quarter Horses tend to be easy keepers.
I would just like to say that if you were going to get a companion horse you might want to get one that can't be ridden because of an injury or an old horse !! I just say this because you might want to give a horse a chance because they aren't as likely to find a good home because they can't be ridden!! Just a thought :)