BASIC has lots of different dialects. Anybody know which one this is, and what modern choices would be compatible with it?

I don't see too many quirks in the listing, so most any classical BASIC variant should handle it. Like PC-BASIC[1], FreeBASIC[2], or the venerable GW-BASIC[3]. (The later I think you need to run in DOSBox though.)

I did notice one unique keyword that should be easy to fix.

    6200 PRINT "TYPE "; S$(56)
    6210 B3 = CLK(0)
    6220 INPUT C$
    6230 B1 = CLK(0)
    6240 B1=((B1-B3)*3600)=(D9-1)

I couldn't find 'CLK' in any of the BASICs I know of. Seems from context to be a time function. My guess is it returns number of seconds since system boot, or program start.

[1] http://www.pc-basic.org/

[2] https://www.freebasic.net/

[3] http://gw-basic.com/