Should be just timothy (or just Orchard grass, Oat, Meadow, etc). Mix bales are often mixed with alfalfa and its best to not give alfalfa to rabbits over 6 months due to its high protein and calcium content.
I would go with 2nd or 3rd cut depending what you can get your hands on. I generally prefer to pick it up when its been recently been brought in so I know how its been stored. But thats not always possible when you run out in the winter months
Theres nothing wrong with buying any of the cuts as long as the hay still looks good, smells good, has been stored dry, has not gotten wet, feels okay when you stick your hand in the middle, etc.