Some side to side movement is normal, but it should not twist or have up and down movement. The original Honda shop manual is very good and worth the money if you plan to keep the bike. One thing the shop manual will tell you is the crankshaft assembly is a maintenance item that should be replaced every so often (can't remember the hour interval).
FWIW, complete CR250 crank assemblies (crank, rod, big end bearing) are not very expensive. I think I paid $160 for a brand new Honda OEM assembly for my '99 a few years ago from Mach 1 Motorsports. Service Honda can also get you a good price. On a CR250, by the time you buy just the big end bearing, find someone to split the crank and re-assemble, ship the crank, etc... you might as well just get the peace of mind and convenience of ordering a new Honda crank assembly, IMO.
When I did mine, new right and left side crank bearings were also not too bad ($30+- each side). The complete gasket kit is maybe $70+-.
The reason I had to repair mine was the big end bearing let go and trashed the right side of the crankcase (another $160). Had to put in a new piston kit, too. Luckily, the cylinder, head and powervalve assemblies were not damaged by all the big end bearing bits.