10 splines would seem to indicate you've probably got an ISIS crankset. Another characteristic that might help you identify an ISIS spindle is that the valleys between splines are rounded. You can do a Google image search for ISIS bottom bracket and visually compare the pictures to your bottom bracket.

There are other splined interfaces, but they generally have differing numbers of splines. Shimano's Octalink had eight splines. Truvativ Power Spline had 12. There might've been others I'm not recalling offhand.

ISIS is a dead standard, so it might be a challenge to find a crankset to fit your bottom bracket with the right chanring sizes and arm length, and in your desired price range. My suggestion, since bottom brackets are generally inexpensive parts, would be to pick a crankset with a common bottom bracket type, then buy a bottom bracket to match your new crankset. Going this route could be cheaper than sourcing an ISIS crankset and it'll give you more crankset options to choose from.