I have a 2.5 gal with a betta. im adding 2 shrimp come christmas. i will O.K the idea of u putting in shrimp. just a few things to take note of
1) they like planted tanks, but its not required. but a huge bonus!
2) make sure they get enough food.. bits of algea alone from a 3 gal wont completely sutaine them
3) be ready for the risk of your betta attacking and eating them peice by peice. make sure to watch carefully (STARE AT THE TANK FOR AT LEAST 5 MIN WHILE AND AFTER ACCLIMATING for signs of hatred from the betta ) look at the tank often the first day or so, and be wary the whole first week. after that, i would let my guard down a bit. be ready to take them out if anything happens. put them in another filtered tank if you have, and if you dont be ready to return to store.
4) this is also what i will be doing :)