I have no advice on where to make your purchase, but yes - if the battery terminals are the correct type and location, the battery is the correct size, and the battery has enough power, it will be fine.
Your old one probably has a size code that will make it easy to pick out a comparable replacement (most MR2s use a "Group 35" battery I believe).
You can probably find more information than you'd ever need at a vehicle-specific enthusiast forum such as
http://www.mr2oc.org