Check your domain and see how many other domains are using the same IP address, most likely on shared hosting like hostgator you will find a very large #, easily 1000 or more. You can guarantee that with all those domains there's gonna be spammers and infected sites being hijacked for spam. You are never going to have reliable deliverability that way.
I just started using google apps for business, it's fantastic. $10 per license, Unlimited storage per user with 5 licenses or more, ($5 per license if you don't need the unlimited storage) so you can ditch dropbox, since you won't need it.
Each license can use up to 30 email aliases, so
[email protected] can also send and receive from
[email protected],
[email protected],
[email protected] etc. and those aliases are very handy, they can be added and removed very quickly without adding and removing licenses.
Users can log in through the regular gmail interface or use a client like mozilla or outlook.
You can also do a free trial for 30 days and see if it works for you, personally I think it's amazing, well worth the money.