If you go with a cheap hosting plan, you will more then likely be running access 2000 which is not bad just so so IMO.
If you go with a cheap hosting plan that does have MySql chances are they have it so loaded, with connection. That it will perform just a little better then access.
I have ran this forum on both access and MySql and even thro I feel the MySql does run better. It all go back to your hosting company, I had to have my hosting company move me to two other servers. Before I found one that was not so loaded that I did not get a timeout from waiting for my connection.
I believe this forum will take a high traffic load as long as you are with a good hosting company. Soon I will be moving to a VPS server where I can run SQL 2005 Express. Guess will see how it runs with that also.
You get what you pay for buy cheat hosting and get poor service.