I was thinking that I would do so. I've been told to stay away from PA mixers when using tape, yet most of the 16 track mixers I see are counsels which are sorta out of my price range for now or they are PA mixers. Is there any compromise in a situation like this or will I just have get one or the other?
PA boards usually don't have the monitoring facilities for multi track recorders but it's not a universal rule that they don't.
The mixers I was originally mentioning were marketed as dual purpose, which means they had to sound good, be reasonably clean and quiet, have the full monitoring facilities needed for studio recording and be built rigidly enough to be thrown into the back of a van to do double duty for small working bands that needed a reliable PA board for their live shows. So yeah, that's not horrible advise you previously received but its not a carved in stone rule either.
Soundcraft might be another brand to keep your eye out for as they too made some very capable recording/PA boards back in the 80's and 90's that were built even better then the TASCAM and Ramsa boards such as their 400 series boards which saw a lot of double duty in PA and pro studio use.
If you have enough time to do this, the right board will probably come along. But if your funds are limited and you need to get something right away, you'll probably end up grabbing something that will have compromises. That's between you and your wallet and watch.
Also keep in mind that any mixer which was originally priced at three to five grand when new and is being offered for under 200 bucks is probably going to come with problems like dead channels, busted off knobs and switches or weird ground hums or buzzes and especially so if they were PA boards which get abused from rough handling and inexperienced sound guys who fry it with overly hot signals or dump their beer onto it. Recording boards tend to be respected by their owners a fair bit more. So if you're not a technician who can do your own repairs, think about what the real cost of a $150 mixer is by the time you pay a technician 100 bucks an hour plus parts to fix it.
As carpenters like to say, measure twice, cut once.
Cheers!