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I would do about a 50% water change with some thorough vacuuming - it sounds like there might be some uneaten food in the gravel. Use a good quality dechlorinator for your new water (I like Seachem Prime) and make sure its the same temp. Don't touch the filter, since that's where the good bacteria is growing.
Bring a cup of water to a non-chain store (Unique Aquaria in Boston, Uncle Ned's Fish Factory out in Millis, Lovely Pets in Quincy, etc (Local stores list)
) and tell them what's going on (maybe print this page so you don't have to re-explain everything ). They should be able to do a quick free water test to make sure nothing is amiss.
Adding a bacteria booster like Stability or EasyStart wouldn't hurt but may not be needed.
Then I would add the betta, and add nothing else for about a month.
Feed him (or her) just 2 pellets of food per day - their stomach is the same size as their eyeball.
Then add maybe 2 neons (or cardinal tetras, which are often hardier and look even nicer).
Give it another month - then add 2 more neons or cardinals.
after another month add 2 more.
Feed the tetras about one flake per fish per day - again, stomach = eyeball size, they are very small.
If you have multiple kids looking for fish at the same time - I generally add about 2 fish per month for a 10g tank. a betta and a cory cat would work (add a few more cory cats later). Or two female bettas or two cory cats.
I'd save the neons or cardinals for at least a month down the road - they are much more sensitive.
Rain forest fish like "slight acidity" and most of the "community" fish in stores come from rain forests (tetras, barbs, cory cats, bettas, etc) - plus ammonia is less toxic at lower pH. The "slight acidity" of your water is typical for Metro Boston region and actually good.
Your water probably has a high pH but low alkalinity coming out of the faucet - so the pH starts high but drops.
Once you have fish in the tank, you'll want to avoid changing more than about one quarter (just over 2 gallons) at a time so you don't shock them with a pH 'bounce'.
I think a balanced 10g tank can easily handle about 8-10 tetras, or 6 tetras, a betta, and a trio of dwarf or pygmy cory catfish, etc.
Looking on my desk here at my office, I have about 16 micro-rasboras (10 kubatai rasboras, 3 chili rasboras, and 3 emerald dwarf rasboras), some cherry shrimps, a panda garra, and young ancistris pleco -- all in 10 gallons. The rasboras are a little smaller than an adult neon or cardinal tetra, but not much. The panda garra probably has the same body mass as a betta. I change about a quarter of the water every few weeks, I feed very lightly (they don't eat on weekends) and everybody is healthy and happy (I see some courtship behavior from the emeralds). However, I stocked the tank slowly, and I also have the safety net of live plants - which utilize much of the fish waste as ferts. (to be honest - I didn't really notice that I had THAT many of the rasboras in there until I actually counted them)
Why did I recommend a non-chain store ? Many of us in the club have worked at a chain or "big box" pet superstore at some point in time. However the chain stores tend to attract people who are also applying to Staples, and Best Buy, and Pizza Hut, etc, and then "teach them about pets".
The small "mom-and-pop" stores tend to attract people who are looking for a place to talk about fish with other people and by the way, get paid for it. People who have been doing this for many many years (decades for some of us) and who got tired of arguing with the mgmt of the publicly traded companies who put stock price and bottom line above animal welfare. I work weekends at one of the mom-and-pops and I can tell a customer "no I won't sell you that fish, it would die in your tank". And the store owner likes the fact that I lose the sale but save the fish (and often create a long term relationship with the customer).
Its new, its improved (its still a work-in-progress)