Aeration- Usually, if you have enough filtration (with power/hang on the tank filters) you will be ok with aeration... I usually like to reccomend 10gph (gallons per hour) per gallon of tank volume...i.e. on my 10gl tank I use a single 100gph filter (penguin mini). On my 20gl I use 2, 100gph filters, etc. By splitting up the filtration into 2 filters (for a 60gl like yours, I'd use 2, 300gph filters) you safeguard youself against a filter failure and you ensure that all areas of the tank get water movement.
If you have some areas that still aren't getting enough water movement (dead spots), I'd suggust placing your airstones/ornaments there. i.e. if you have a filter on the right hand side of the tank and nothing on the left, place the airstone on the left.
Usually air pumps will give you a "tank size" rating or a rating via how deep the tank is...ie. "this pump is suitable up to 24" tank height". I'd suggust going with a better air pump rather than going with a cheaper/smaller model (some air pumps can run multiple units at the same time). Also, get a safety or check valve for all of your air lines/ornaments/stones.. It basically looks like an airstone w/ outlets on both ends... You place it midway between the pump and airstone/ornament. It prevents the water from going back down the line into the pump in the event of a power failure.
Stocking: I have kept bettas (both male and female) in my community tanks and have run into few problems, with a few exceptions... I wouldn't suggust keeping a betta with any other anabantoid (i.e. gourami, paradise fish, etc.) or any other primarilly surface-dwelling fish...like hatchets that tend to stay near the top where the betta's main "territory" is. I would also avoid any similarly long-finned fish that the betta might mistake for a rival (i.e. long-finned danios, rasboras, etc.) Lastly, avoid any very agressive or highly active fish that might "snack" on the betta's fins... i.e. medium-sized cichlids like the firemouth, zebra danios (they are hyper and look for things to do, like nip the betta) or tiger barbs (who don't work well with MOST other fish).
That said, for a 60gl with a betta, I would reccommend the following options for you to look into:
1. A group of bottom-dwellers... i.e. cories (panda, melini, peppered, aneus, etc.) loaches (3 yo-yos, 3-4 dojos, or 6-8 kuhliis).
2. Schoolers- Instead of the very hyper danios or ultra sensitive (and usually poorly due to inbreeding) neons, I'd suggest:
- cherry barbs (a group of ~5 males and 6 females will give you quite a show with their bright colors. They are very peaceful and don't "school" a lot).
- Serpae tetras (if kept in a large group i.e. 8+ they keep to themselves, don't school a lot, but do display a lot)
- White cloud mountain minnows- one of my all-time favorites... similar size to neons, but prefer cooler temps (i.e. 76-74f). Red fins, and the males get a "bronzy" color to them.... They school, can be fast movers, but are very peaceful and display (by flicking their fins) a lot. A group of 12+ would make an awesome display
- praecox (neon blue dwarf rainbows)- GREAT fish! If you can find them, neon blue in color, bright red fins on the males w/ yellow fins on females. Peaceful, active, display and "flash" when you have a mixed sex group. Highly reccomend.
- Glowlight tetras are also cool fish. They look similar to neons in that they have a neon stripe down their sides, but the strip is orangy-red and they have orange eyes. Hardier than neons and a tiny bit bigger. They aren't as fast moving, but are nice fish.
- lemon tetras and black neon tetras I have also heard good things about, but haven't kept personally.
You can mix a couple of the above... i.e. a group of slower-moving cherry barbs and some white clouds, etc. It's just important that schoolers have a large-enough group of their own... At LEAST 6, preferably 8-9+ of each species.
3. "show" fish- although the betta will be a "show" fish due to his/her personality, if you want a showy fish for the bottom of the tank, either a bolivian ram or krib...both dwarf cichlids might work well.
4. Algae crew- Wait on this till you have algae...lots of algae, then I'd either go with a single bristlenose or ~4-6 otocinclus catfish (the smallest pleco and live-plant friendly.