You could get a small trio of cory's like Julii, Peppered, Albino's, Panda and Bandit's. If you do get a trio then only get one type because the different types don't shoal together. Cory's need to be together for social reasons and will usually become depressed or not active when not with at least three or more. Also it's a good idea to have a nice fine substrate. If you've got regular gravel that isn't smooth i would not suggest getting Cory's because they've got barbel's around their mouth and if those get damaged while rumaging around then the fish could get infected, leading to death because you usually don't look at barbels lol So that's something to consider as well.
Yeah I don't really like Ghost shrimp either honestly. But if you can find Red Cherry Shrimp, that might be able to work but of course depends on the Betta. My long finned boy isn't fast enough to catch all of them so if you put in like 10 or so, Maxx probably won't be able to eat them all. However that's me assuming Maxx is a long finned Betta. If he's plakat or a shorter DT then I wouldn't suggest shrimp at all, even Amano shrimp which usually stand up for themselves can become Betta snacks
saw that happen with one of my 3 month old Betta's who is still tiny!
But for the most part you want to look for bottom feeder fish, unfortunately either most get too big or your need to get a school of them. You could for now get a tiny Pleco and then when it starts to get too big, find a home for him/her or donate to your local petCo. But keep in mind that ALL algae eater's create lots of poop, doesn't matter what kind of algae eater they are or what types of algae they eat. Not all of them eat all kinds of algae either :-/
Something you might want to look into are Bristlenose Pleco's, they only grow to 4 inches but you'd still have to find a new home for it as in a 10 gallon it won't be able to grow much. But for the time it will eat most/all of your algae but you will have to supliment with cucumbers or zuchini or lettuce. There's other veggies you can feed them too and mine would eat a whole slice of uncooked cucumber in two days lol, crazy! but she did really well for the algae in my 33 too.
Feel free to ask questions if you need ^_^ I know I can write novels sometimes haha