As others have mentioned, all you need is a straight stitch. As for machine, here's a free piece of advice: get a vintage Singer 66, circa 1930s-40s.
Let me explain - I got lucky and wheedled my (late) grandmother's Singer 15-91, circa 1949, from my mom, who had had it since 1960. It was in mint condition, except for a worn bobbin wheel that needed to be replaced. It also needed to be oiled and undergo some light cleaning (ie remove built up lint).
Since I had re-built a number of cars when I was younger, and am pretty mechanically inclined, it was a piece of cake to restore this baby to pristine condition. In the process of replacing some parts & working with the machine, I became more familiar with some of the other vintage Singers that are favorites of collectors.
There are a handful of vintage Singer machines (221, 201-2, 15-91, 301 & 401) that collectors tend to focus on, hence they bid up the prices. The model 66 looks similar, and is a sturdy, high-quality machine, but due to being built in such large numbers, and being more of a "home ec" machine in its day, tends to be universally ignored.
Every now and then I will peruse CL out of curiosity, and sure enough, there are usually a number of 66s (also 3/4 size 99s) for sale between $50-100. (It's rare to see the machines collectors like listed above on CL since they are usually cleaned up and sold on eBay.)
There's no need to get one that isn't operational/needs work, or one listed for a higher price by someone who has no idea that it's not worth a higher price. Just keep your eye on a one that is in working condition, and if you get real lucky, one that still has its original carrying case.
Here's a picture/link of one that is for sale on CL in SoCal:
And here's a link to a review of the Singer 99 (3/4 66):
The thing about older Singers is that there are (a) zillions of parts available; and (b) zillions of modern knock-offs that still use these core Singer bobbin & needle standards.