Null Modem is quick and easy.
Well, quick and easy in comparison to sneaker net, for sure.

ParNet is faster than a Null Modem, but not by too much, and ParNet is a bit of a fragmented system, as IIRC, there were two different revision ParNet cables, and one worked much better than the other. And worse, I forget which worked better, and neither are real easy to find nowadays. Null modem is the safer choice. And ANY of these solutions are painfully slow in comparison to something like a 2065 ethernet card. ;-)
the serial port on an amiga 1200 runs much master than a standard serial port on most pee cee's
This is wholly incorrect. Even the serial port on my oldest PC (Pentium 1 @ 133mhz) soundly trounces any Amiga serial port. The Amiga serial port is routed through the chipset rather than a dedicated UUART chip, and is slow as heck. The maximum you can expect without errors is 19,200. (And, honestly, only my 4000/060 could sustain that -- my A1200/030 had troubles at that speed.) If you use an error correcting system (highly recommended, even at lower than 19,200!) you won't benefit much by trying to go to 38,400 as the error/retry rate starts climbing high enough you get a slower overall throughput.