Would suggest you go and test some different models, take some scraps of fabrics that you maybe using now and in the future. Make a list of features you want on a machine, vinyl usually you need a teflon foot and possible some Water Soluble Stabilizer to help it glide, size 11 needle.
Buy the best you can afford, get the most bang for your dollar. The advantage of buying from a dealer is they may give you a few lessons on the features of the machine.
Curious,
What type of old machines do you have?
Would they be worth having them serviced? Are you using the correct needles and bobbins on machines, like Singer machines usually require Singer needles.
Hoping others may have more input.

I have a Brother (low end - I think there's something wrong with the bobbin thingy) that's not all that old and two old Kenmores (very old - one won't do long stitches and the other is currently not working at all). I'm using the bobbins that came with them and I have no idea on the needles (my MIL gave me the Brother and loaned me the other two and I'm using the needles that she sent with the Kenmores). It might be worth it to fix one of them, but I'm really short on time. I only get to sew for about two hours a night and I only have a week to get a shirt, a pair of pants, a vest and boot covers done (oh, and did I mention I'm pretty much a beginner, so it takes me a little longer than it would an experience sewer.)

I think I'm heading out today to visit a dealership or two to figure something out.

Thanks so much for your help!

I don't know if this will help, but my very first machine was a Kenmore. It was in 1966 and I was 15(yes, I'm ancient!). It had straight, zig-zag, forward and reverse...that's it. I used that thing for several years, then my mom passed and I was left her Singer with a few more bells and whistles. But anyway, unless yours is a lot older than that, mine did long stitches(basting stitches)just fine and I made a lot of clothes with it.
If you took your Kenmore to a dealer/service center to get a tune-up(sounds like settings are off), which shouldn't cost that much, maybe they could give you a loaner to use until you get yours back. At least you would have a working machine for your project, and the Kenmore should be good for many more years.

One more suggestion...it took me a while to find this, but a machine basting stitch is about 6 stitches per inch, or 4mm. You can check your stitching to see how far off it is.May be it isn't that far off and adjusting the tension may make it work for you.

I agree may be worth having one of the Kenmores looked at, although I do not own one some of them were not bad machines.
The Brother if it is the Bobbin Case, Not that expensive to replace.
Frustrating for a beginner to have to use a machine that is not working well. I am sure you will make the right decision on what to do.
Do you have any friends that sew maybe you could use their machine until you decide what to do.

LOL noinwi although I have some top of the line embriodery/sewing machines and sergers I still have my Singer 185J I got for a graduation present, it sews leather, upholstery and silk, yours is fancy, no zigzag on mine.