carborundum stone from hardware store, has 2 sides, can't miss it. Get a bottle of oil, it will last forever, doesn't take much, and you are still probably at or under 10 dollars.
That's how I started, if you're just getting started collecting knives and you say ya can't afford too much for a sharpening system, I can almost guarantee that you aren't buying knives with any high end after steels so a carborundum stone will suit your needs.
Wet/dry on glass can give a pretty damn good razor edge.
But most important, technique is king. Not the tools.
This is great advice and considering the knives you're probably buying they'll give you plenty of opportunity to practice your sharpening skills at a reasonable cost and developed all the technique you'll need.
Last piece of advice, when buying stones for free hand sharpening, buy the biggest, best quality stones you can afford, this is always gonna be a balancing act between cost and size but that is more a personal choice. If I had to favor one over the other if go with quality over size but there is a compromise, it's just determined by the average steel your knives have and your experience.
Buy a good 6X-8X loupe and study the type of sharp edge you want to attain, learn what a sharp edge looks like so you can compare results and practice, practice, practice. The only way to get proficient is practice, sharpen everyone's knife you know, maintaining angle should become second nature.
By the time you go through all of that, as your skill improves, the quality of the steel used in the knives your collecting goes up, you'll probably realize that there is a no more efficient, more economical sharpening system than person practiced in the art of free hand sharpening.