How low budget are we talking here? 50$? 100$? 0$?
I would suggest you look for a guitar that has “low action”, this means a small amount of space between the strings and fretboard. Low action guitars are easier to play, softer on the fingers. Also, using nylon strings instead of metal strings is better on the fingers, it produces a bit of a different sound but that’s irrelevant when learning.
Hands down the best deal you’ll find for a guitar is on used sites. You get the biggest bang for your buck, as people are trying to recoup their failed investment. But the flaw is that you have to inspect each guitar before buying it, which takes time, and you have no idea whether you will like the brand before having invested the time in inspecting it.
The benefit to going to a guitar store is you can try out many brands of guitars to find one you like. But then you have to pay retail prices on both the guitar and the accessories. Sometimes they have consignment guitars, and while that provides some discount, it’s not the discount you’ll see from Craigslist.
So I say combine the two methods. Go to a guitar store and spend hours trying all the guitars till you find a few brands you enjoy playing. Since your price point is low I’d stay with the entry-level ones, but try the medium ones too cause you’ll never know what people will sell on used sites. Then keep an eye on the used sites for those brands of guitars, and go visit it and try it on.
When I bought my guitar, I asked for advice about brands on another asking-question website, so I already had a few brands in mind going in to the store. For me, buying a Canadian-made product built with Canadian wood was a very important criteria. My budget was around $250CDN, so above entry-level but nothing really fancy. After trying on a bunch of guitars and playing a bunch of diddies, I fell in love with my guitar… I still remember that day, it was love at first sight, just a glance over in the wrong direction and BAM there she was looking all beautiful and sassy. But I was lucky to have the luxury of being able to buy her instead of simply researching at the guitar shop. I admit I was in love and let my heart decide the purchase over my brain trying to tell me to get a better deal.
I would go ahead and post a wanted ad for a guitar that has low action and a low price, in addition to keeping your eye out for other ads posted. You might just get a response from someone who has a few guitars in their attic, et cetera. You could also offer to barter in your ad, which may make the transaction more appealing for a potential seller, provided you have something to barter with. In this economy though it should not be hard to find you a good guitar!