The hay that is the cleanest and most affordable for you.
I know that sounds like a cop-out, but that’s really what it boils down to. Unless you have an air fern, or a really hard keeper, the mature, moderately working horse needs good hay - doesn’t have to be GREAT hay that you’d want to feed an upper level horse or late-term broodmare, but should be more than “busy hay”.
If you need significant calories on top of that, then look for better hay.
1st, 2nd, etc cutting, is fairly relative and is based on the ideal cutting times. 1st cuttings tend to be a bit weedier. But a late 1st cutting can also be overly-mature.
Orchard and Timothy are good choices if you have them available. But there are lots of Bermuda varieties which are good as well, such as Tiftons, Bahias, and others.
Because of different nutritional profiles, if you can find mixes that’s even better. Around here, fescue and orchard is a common mix, simply because fields planted with OG end up with some to a lot of fescue in them anyway, unless regularly tilled and re-started.
If your horse is a harder keeper and you’re looking to reduce concentrates, then it’s better for him, and usually easier on your wallet, to find a hay that is up to about 20% alfalfa. Timothy is commonly mixed with it - T&A hay. I’ve seen some Orchard/alfalfa mixes. Or you can buy bales of alfalfa to supplement the grass hay, but mixes tend to be better in terms of what gets eaten since it’s all mixed in - feeding alf separately often ends up with that being gobbled up and the grass hay begrudgingly eaten :lol:
It sounds like you just need to find whatever is easily available and affordable that is also clean and fresh-smelling, and go from there.