How do I stop felt from puckering around my stitches?

The white on green was the right call, it reads so much cleaner than dark thread would have. And the running stitch lines look nice and even now, so whatever middle ground you found on tension clearly held up through the whole piece.

Since you fought that puckering early on, for anyone who lands on this thread later, felt does that because it has no woven grain, every stitch just displaces the fibers around it. The three things that help most are shorter stitches, less tug on each one, and a bigger needle. A larger needle opens a little channel so the thread can sit between the fibers instead of dragging them together. That alone kills most of the ripple on felt. On your original hoop question, snug is right but drum-tight is too much for felt. Unlike woven fabric it doesn't need to be pulled hard to stay put, and a bit of give actually lets it relax back flat when it comes off the hoop. Stabilizer underneath is optional for running stitch, felt is sturdy enough on its own for that. It only realy earns its keep with dense fills or satin stitch, or if you're working on thin craft felt that's floppier than wool blend. If puckering shows up again on a future project, a scrap of tissue paper behind the stitching area and torn away afterward is an old trick that works well. For the framing, since it's a gift, just make sure the felt is laced or taped at the back of the mount rather than glued at the edges only. Felt has a bit of stretch and glue-only mounting can sag or wave over time, expecially if it hangs somewhere warm. Laced edges keep that face flat for years.

Good finish for a first piece, and keeping the black on the red was smart, the contrast balance looks right.

One thing that saved a felt wall hanging I did last winter: after I took it off the hoop I laid it face down on a towel and pressed the back with a warm iron, no steam. The ripples that were still hanging around flattened right out. Felt can take more heat than you'd think but test a corner first, cheap craft felt can shine up on you. I've also had luck pinning a stubborn piece to a cork board overnight with a light mist of water. Between that and the pressing it came out looking flat as anything for framing.

Following along here as someone who's only ever stitched on aida before. Felt has been a weird learning curve for me, mostly because it moves so much more than I expected. Question for anyone though, when you do the tissue paper trick, does it get stuck in the stitches when you tear it away? I tried somthing similar with a water soluble backing once and picking the bits out was misery. Also curious how folks finish the back of these, my felt piece has all my knot tails showing and I have no idea if that's normal or if I should be burying them somehow.

Gotta push back on the bigger needle advice. On felt I've found the opposite works better. A fat needle punches a chunky hole, and in a napped fabric like felt those holes stay visible and can actually drag more fibers around as you go. Small needle, thin thread, that's what kept my running stitch lines flat on the felt ornaments I did last month. The real culprit for ripples is almost always tug on the pull-through, not needle size. Keep the tension light and let each stitch sit loose, and the felt stays put.

Been doing felt since the 80s and one habit stuck with me from my grandmother's pattern books. She always let the finished piece sit under a stack of books overnight before mounting. Felt holds memory in the fibers and a night of flat pressure settles any lingering waves without touching an iron. I still do it with every felt piece before it goes in a frame. Old school but it works. The other thing I learned the hard way on a table runner years back, don't handle the finished piece much before you frame it. Every pass over the felt smooths the nap one direction and can pull the whole thing out of square.