You're not going to get your server requirements met in any shared hosting account.
No VPS or dedicated server will meet those specs out of the box unless it is custom configured by the host. The hang-up will be PostgreSQL and DBD-Pg (forget about the commercial apps - nobody will put those on a VPS due to licensing costs).
Most hosts use MySQL since it is more widely used than PostgreSQL. It can be argued that PostgreSQL is a more robust platform, which is why some people prefer it.
The other thing you need to **seriously** consider is how you're going to secure it. Web based accounting apps are hacker magnets. Unless you are a security wiz, they will find a way to break in and do damage. I would never run such a thing on a VPS or shared server for the simple fact that the hosting company staff could look at it. All it takes is one bad hire at the hosting company to make big headaches for you.
You should really be looking at colocation for something like that. Setup the server yourself and send it to a reputable colocation facility. Of course, it's always better if you can avoid doing that type of stuff on a publically accessible web server and do it on a private server on your own LAN instead.