I have sewed on many old machines and new ones. It all depends on how much hassle you want to deal with. On the low end a used good machine is your best bet---the new brothers and janomes and kenmores will work, but will be less pleasurable to use.
In the end I bought a newer Elna, fairly low-priced all mechanical (3005), which is made by Janome. It is not because the old ones haven't worked well, but because the newer ones are easier to use. It has a _good_ drop-in bobbin (not like the 70s singers, or others that have automatic tensioning: they are impossible to get consistently balanced stitches in fabrics of varying thicknesses), a needle threader, easy foot-pressure regulation, thread cutter, internal spool holder, all kinds of useful feet stored right in the box, and all the stitches necessary for wovens and knits of all weights. It is also incredibly strong and quiet, and will require little maintenance. It carries a warranty on the mechanics for 25 years.
Lightweight nylons are tricky to sew without having the seam pucker. If you don't mind the look, a puckered seam does not affect the performance of the fabric. For perfectionists like me, use the lightest thread, supplest thread you can---100% poly continuous filament spun embroidery thread seems to work well, as seam strength is not so crucial---with the smallest needle, so that you can work with the lightest tension you can. Adjust the bobbin so that you can sew at 1-2 on the upper tension dial.
Stretching the seam lightly will work. A quilting (straight stich) foot will help. A walking foot helps too, and can help in reducing the number of pins you use. This is what AYCE at thru-hiker recommends. It takes a few projects, though, til you can sew very much without pinning and get a good product.
With silnylons, pinning is necessary unless you have a walking foot. It is very hard for this slick material not to slide against itself as it passes between the gripping feed-dogs and the bottom of the presser-foot.
Hope this is helpful.