"What types of applications do you feel can be ran efficiently with MS Access?"
None? :-)
MS-Access is a very very small, very slow flatfile interface.
Why doesn't your current host support mysql? it's free! 🙂
"Is it practical to run something such as a message forum or link database using MS Access?"
Nope.
MS-Access doesn't like many records, and it doesn't like high-concurrency.
Demand mysql or move to a different host.