I would probably plan one or two weeks worth of meals and deliberately buy what we need for those and then buy extra for the other weeks.
We generally use more chicken than other meat so would probably buy enough for two or three meals using chicken every week, therefore 8 or 12 meals using chicken. Mince quite often so buy enough for one meal a week, therefore four lots of mince. A joint for once a week, so 1 beef, 1 pork, 1 gammon, 1 lamb for example. Maybe steak for once a month, pork chops/steaks twice a month, burgers once a month, sausages once a month etc. That is 21 to 25 lots of meals bought for there!
You can add it all up to have a rough idea how many meals you will be buying for without actually knowing exactly what you are having each night. Make sure to take into account any vege meals you'll have so don't need meat that day, any pasta, pizzas, fish, take outs etc too.
If you have meals you know you'd eat more often than once a month if you have the meat in anyway I would make two or three portions on the first night you have it and freeze the other portions e.g. three portions of chicken curry in week one so you have two to freeze to make it easier later in the month or keep them for next month; two meals worth of lasagne so you have one for a couple of weeks time. If the raw meat would be taking space in your freezer you may as well have the cooked meals frozen instead, much more convenient.
Just buy the meat to fit your preferences, it is not worth buying chicken for 20 meals if you're not keen on it and only buying pork for two meals if you love it. Of course, if you love steak and chips but your family aren't as big fans you could always 'accidentally' order a freezer full and say you have to eat them up before buying more meat!