It won't be easy to get usable hay equipment with a budget of $15k for a round baler, cutter, and rake.
A 4x5 or 4x6 round baler that's not broken or completely worn out generally starts at $15k around here, although you might get one for closer to $10k if it's a twine only model as nearly everybody around here net wraps so they can store bales outside. 53 PTO HP and a 4500 pound dry weight tractor might do okay enough if you are doing dry hay on flat ground, back off on the bale size and density if needed. Smallest tractor I've ever run in front of a round baler was about 65 PTO HP and it did fine.
You could get a used sickle mower that works for $1000-1500 or so. Haybines are generally $3000-5000 in running condition (depending on size and condition). I've never cut with a plain sickle but I have with a Haybine. They are certainly usable, but nowhere near as fast as a disc mower and can get jammed up with clumps of hay that won't faze a disc mower. You will be spending at least $6000-7500 on a 3 point disc mower that's not complete junk. I would not buy a disc mower that's not in good shape, particularly if it's a gear bed mower like a Kuhn, else you will be doing some very expensive repairs. You don't have enough power to run a disc mower-conditioner (Discbine, MoCo) or one of the trailed disc mowers that's larger than 10 1/2'.
A bar rake in good condition will run about a grand for a Deere 660 or 670 and about two grand for a New Holland 256 or 258 or one of Deere's newer bar rakes that are much less commonly seen (662, 672, 64, 72.) Essentially every V wheel rake I've seen under about $3k is either broken or had been broken and welded on with varying amounts of skill. The inexpensive ones have the wheels mounted in pairs to little lightweight U-shaped frames, these like to bend and break. The heavier ones where the wheels attach individually to a toolbar-like wing generally start at $5-6k used but they hold up a lot better. Given your budget, just get a bar rake in good shape and call it a day.
