I have had several Beta over the past years and my kids want a different kind of fish. The Beta worked because they didn't need a filter or aeration. Our tank is 3 gallons, some decorative plants, and a temp regulator. What fish would be good for this set up? Not interested in purchasing a bigger tank or air system they always break on me. Thinking two or three fish max.
Unfortunately, there is no fish that can thrive in a small container of its own filth with limited oxygen for any length of time. I am sorry to say this, but even your beta fish needed filtration once it arrived at its new home. Unfortunately, I suspect that's why you've gone through several of them in the last few years. Betas live 4-6 years upwards of 10 years in a domestic environment. It's unfortunate that pet stores continue to sell fish and bowls as zero-care setups explicitly.
Beta fish and (to a lesser extent) your common goldfish are able to survive adverse conditions for a short period of time. That's why they are displayed that way. But understand that by keeping them in these conditions is only giving them minimal life support; barely. These no-air, no-sanitation habitats are essentially subjecting them to becoming short-lived, disposable pets struggling on borrowed time.
To be fair to your question, if you pick virtually any small, non-social aquarium fish rated for "beginners" — one that will never grow and one that doesn't mind living in near isolation — it is possible to maintain a severely under-stocked tank without a filter… but that's provided you follow a rigorous routine of frequent water changes and water conditioning that is outside the scope of this question.
But honestly, for want of a simple sponge filter and an air pump that should last you for years, I wouldn't even try.
I agree that this tank is not suitable for fish.
But perhaps you can consider getting shrimps? It are active animals which are also fun to look at. They're perfect for small, low maintenance tanks.
Even though they will also need some filtration. Best is a sponge filter with an air pump, that way the little shrimp won't be sucked into the filter.
I've got a 30 litre tank (8 gal), with neocarina heterepoda shrimps (cherry shrimp). These are ideal starter shrimps, because they are easy to keep & breed.
They're group animals, so to start you should probably get around 20 of them. But after a couple months you should already have plenty more. I started 7 months ago with 25, and I think I'm now well over 70 (it's getting to difficult to count).
If possible, check if nobody in your area wants to sell a few, instead of buying them in a pet store.
In Belgium, pet stores usually charge up to €2/shrimp. I've been able to buy mine for €0.50/shrimp.