Oh, forgot to say: If you do try MS Paint, you simply can use
ctrl-c and ctrl-v to paste the gifs from other apps. Also, you
might enlarge the bitmap (the white area you are working in)
ahead of time using Image/Attribute toolbar. Make it big -
enough to paste in all the pieces. You always can drag it
smaller after you are done (drag dots are at the corners and
sides). Paint lets you stitch together stuff easily and
precisely. I have payware that does this too (I guess Paint IS
payware - sorry. Make it: You-probably-already-have-ware), but I
really like using Paint for this.