TSR is old DOS shorthand for Terminate and Stay Resident. It was a big deal because you could only fit so many such programs into the 80K or so TSR area of your 640K. You could increase your high memory area, to a point. It it got too big you wouldn't have enough low memory left. You needed about 540K to have enough to load enough in so that your expanded memory could function. Boy I miss those days!
But, for the original poster, those days are long over - even on Windows. You don't need any anti-virus software on the Mac. If you have any, it will only cause problems. Speaking of which, are you having any specific problems on your Mac? Memory is really cheap so there is no reason not to max out your RAM. There is no amount of well-behaved software you can install that will overload your Mac. It can handle all of it. If it has problems, there may be one or more programs that aren't well behaved and need to be removed. Quantity is irrelevant, but quality is still important.