Caution: Buzz Killington here again with another boring discussion.
Don't pay as much attention to the name. If you're just going to do this one project and let the machine collect dust, find an older (70s-ish) machine from a known name and buy it for $75. Elna, White, and Singer are all common and bulletproof names from the era. Just like a car, though, they will all have wear items. They all have a clutch, timing, a transmission, and a motor.
If you were saying you just wanted to make some shorts or a set of curtains for your house, any machine will do. When you're doing upholstery/vinyl/leather, you need a motor and transmission that are up to the task, and you have to be sure the clutch is not worn. Otherwise the needle will just stop at the vinyl and the clutch will slip. (My Elna has this problem right now).
Machines can also jump timing which can lead to loose stitches, tight stitches that break the thread, or just clashing metal things. If you buy one and it doesn't present any of those symptoms you can assume it is still timed correctly.
Bernina is known around the world as the industry standard for home and light commercial machines. Be prepared to pay accordingly, but they use incredible motors with tons of torque and the motor spins at a higher RPM with a greater reduction ratio in the transmission. The downside is that if it needs maintenance or repairs, it actually needs a certified Bernina repair person. You might think you can figure it out, but it's like thinking you can rebuild a modern McLaren dual clutch transmission with just a YouTube video.
I have two machines. One is a nearly new Brother that someone gave to me. It is the barest-bones thing they make. It works beautifully on light fabrics like shirts, drapes, and muslin/duck/duvetyne. Give it some denim, though, and you're lucky to get through two layers in a simple seam, but don't even think about a lap seam. It doesn't even have enough torque to break a needle. It is like a Toyota Tercel. It gets from A to B slowly and doesn't do anything else well. The other machine is a 1978 Elna 410 Primula. Mom bought it for me when I was a kid when I joined the 4H sewing club. It is a workhorse. It isn't the torquiest, and it would have a little trouble with thicker vinyl, but it can do it. That is the one that has a bad clutch right now, so it doesn't sew anything much thicker than canvas at the moment. I'm debating fixing it vs selling. It needs to be timed and have the clutch redone, which is likely a repair that costs three times what the machine is worth. This Elna is like an IH Scout; zero glitz, but if you're careful, it will go anywhere you want to go.
Some ideas. This one with the right needle could do the trick: (9) Marketplace - Gently used sewing machine | Facebook
Be aware of plenty of knock-offs. Taylor is a respectable machine. This one is advertised as a Taylor, but it's actually a Tailor. Not terrible, but they like their plays on words. (9) Marketplace - Taylor Professional sewing machine | Facebook
Also, dig into model numbers. If the description includes things like "quilting" or "embroidery" then their emphasis is usually on features and options, and less on brute strength. Quilting and embroidery don't require a ton of penetration power. Often times a utility machine that has "fashion" or "home" in the description tend to be more along the lines of what you want. Fewer bells and whistles, but can sew denim, or slip covers, and thick curtain fabrics.