Neons are nice little fish. They are clean and peaceful and look beautiful when they have room to school. They must be kept in groups of at least 5. That would really max out a 10g. I also don't know if that's enough space to really appreciate the schooling behavior. Hmm. I just love these 'fill my tank' threads. Its so fun to come up with all these different scenarios and see others' suggestions.
I just started a female betta tank in a 10, but you sound like more of a beginner and that's a bit more advanced.
For starters, get rid of that algae eater. There is another thread on here detailing the pros and cons of siamese vs chinese algae eaters and the confusion of the two. Look for it. You shouldn't need one anyway once you learn how to keep your water properly balanced. (Yeah, easier said than done, I know!)Not to mention, that fish may be why your other fish have passed on.
OK, now in my mind, your tank is empty. So, I would start with a few plants for that lovely natural green color. You can get plants going in a 10g with compact fluorescent lights that fit into a standard cover. That's what I did. The bulbs are pricey, but they work and its a relatively cheap endeavor without changing the light ballast.
Then I would get a few cherry shrimp. Shrimp are really fun to watch and easy to care for too. Add a bright colored female betta. This is where I get stuck with this set-up. You have room for about 3-4 more fish. My first vote would be virgin female dwarf platies. Then you don't have to deal with overpopulation problems, but virgin females are virtually non-existant in the stores. (Why don't they DO that? People would pay more for these fish) Or 3 male guppies. This runs the risk of the guppies harassing each other if you get a feisty one. People do male only show tanks though, so you could try it. It would be a colorful and lively tank. Yes, the guppies get my vote for low maintenence.
Although, I don't think you need to completely discount a small school of neons. I would still oust the algae eater, just for space considerations. With neons, I would plant the tank, real or fake, with all medium and light green plants. Plant with space in the middle and around the sides. Don't tuck the plants right against the back wall. I have a school of 10 cardinals in my 75g, they look great swooping behind and around the tall plants. And all green will really cause their coloration to pop out.
I always resort to neons and livebearers. I will enjoy seeing what others suggest. Good luck!