My family has always used a plastic bag, much like those ones you find in the produce section of the grocery store. Then wrap that in butcher paper.
The real trick is to get all the air out of the bag, usually the meat goes down in one corner. Give the bag a twist and double it over its self. Then you place that bundle on a large square of paper, starting in a corner, roll up half way, fold the sides in, finish rolling, last corner gets a nice little fold over and a bit of freezer tape. Sharpe label.
If you are doing bone-in, it is much tougher to keep the air out and the items don't seem to keep as well.
But for burger, steaks, stew meat and roasts this method works like a dream.
You may not care for the use of plastic, but I ate a package of moose burger a few year ago that had been lost in the bottom of one of our large chest freezers. It was over 3 years old and I could not have told it apart from a package a week old. Still perfect dark red.
PS. another plus for butcher paper is over vac bags, which I do use for fish, is that in the freezer a package of meat wrapped in paper can get banged around and it wont poke a hole in the plastic letting air in and causing that horrible freezer burn.