I'm wondering what I should look for in a pony bottle and regulator and if there are certain ones that are recommended.
Regulator: Just about any regulator will do, including used ones. Ideally, some-brand you can have serviced wherever you usually service regulators. The only real requirement is that it works when you need it, but beyond that you don't need a fancy regulator. Keep in mind an "octo" usually is just 2nd stage regulator, that is slightly cheaper than primary 2nd stage reg.
If there are "requirements" for your main regulator for the type of diving you do, such as cold-water diving, those would also apply to the pony.
Whatever regulator you get, I would ditch any unnecessary hoses, and install port-plugs. That means no octo. No inflator hose, unless you use it as a dry-suit bottle. If slung in the front, use either a "button SPG" (no hose) or an SPG on a short 9-inch hose tied so the SPG-face is outwards.
There are also first-stage regulators designed to replace the valve, which are slightly more compact, but I'd probably just stick to "normal" first-stages myself (and DIN if possible).
Pony:
A "pony" is just a scuba-tank, little different from any other scuba-tank, so branding, etc mostly doesn't matter. The main question is size. Most everything below assumes average or better air-consumption, and a diver not prone to panic.
- 1.7cu and 3cu (spare air) - These are dangerously small, and no pony is better IMO. I did test dives with these at 20ft, and they were out of air in no time. They're dangerous IMO, because they give a false sense of security. Without the spare-air, one might at least be encouraged to stick to CESA depths. The spare-air regulators are also very difficult to breathe.
- 6cu - Better than nothing. My testing of a 6cu was about 100psi per normal breath at 8ft deep. I one for travel (because I don't own a 13cu), but also am very mindful of limits, either staying with groups or a buddy, limiting depth (30-60ft) , and avoiding any potential hazards (overheads, entanglements). In an emergency, it's (probably) enough to save your life, but don't delay heading to the surface, and probably skip safety stop.
- 13cu - A good travel-size. Twice the air of the 6cu, but still lightweight and small. You can be a little more confident at depth or while solo-diving, but at around 90ft, you might similarly be finding you need to not delay, stay clam, and skip safety stop. At 120ft, it would be technically enough to save my life (assuming no panic, entanglements, etc), but bottle might be empty by the time I reached the surface. Keep in mind though something like your primary reg failing might cause some degree of panic, and faster breathing.
- 19cu - The 19cu is my "daily driver." It's 50% bigger than the 13cu. Based on my calculations and testing for myself, I could surface from 120ft, with a safety stop, and have plenty of air remaining. Compared to the 13cu, the 19cu gives me an extra degree of confidence that there's never a reason to panic.
- 30cu and 40cu - Get an extra 50% or double the 19cu! 40cu is also a good size for technical diving. If you're a heavy breather or often dive in the 90 to 120ft range, I'd get a 30 or 40cu. The downside is primarily on the surface, due to the extra size and weight inconvenience. It's a bigger and heavier tanks to lug around, to/from dive sites, up ladders, and similar.
Every diver I've met in person, who has a "30 or 40cu pony bottle" always leaves it at home and "doesn't need it this dive." If you carry one, that's awesome, however to borrow a saying from the concealed carry community,
"The 13cu you have on you, is more useful than the 40cu you left at home."
That said, a 30 or 40cu tank is quite practical. I often dive sidemount afterall, which is basically diving with two full sized AL80s (or bigger) which is double the size and weight. I'm just encouraging you to be honest with yourself about whether a bulkier size might encourage you personally to be lazy and leave your pony tank behind.
Lastly, for me, because I dive sidemount, it's silly for me to not use 2x 80cu tanks (or bigger) past 90ft, even if the 19cu is technically enough for an emergency. Since I have 2 full-sized tanks, I can also increase bottom time.
edit: You can also real-world test about how much air you'll need. Dive to the maximum depth you expect to take your pony bottle, lets say 90ft. Swim around enough so you're using air, check your PSI, and then surface normally, including safety stop. Write down the start and end PSI. From there you can calculate how much volume you actually used. Then add some % of air, depending on how prepared you want to be for panic, entanglements, etc.