There are many ways you could go with this. For my first, I went with a simple basic classic design and got a Buck 119. Now its handle isnt for everyone, but its a good material and wont break. The blade on it is nice as well and sharpens easy. Now if I had to do it over again, Id probably scour the internet for a 5 1/4" Kabar which CAN be had for under $50 if you know where to look. I only say that because for some things, I found the Buck to be a bit big and the 5 1/4" is my favorite blade length for survival stuff.
But if you didnt necessarily want a knife and just looking for a survival blade, you could go with a small Khukri blade of a machete. Both of which can EASILY be had for under $30 and still be much higher quality than any knife youll find around $40 to $50 bucks (sounds odd yes, but somehow its true). A slew of Ontario military models (good stuff, but watch the quality control on these), Condor (which is my favorite for quality and build reason), Cold Steel (not great, but cheap and perfectly serviceable), and imports can easily be found for like $8 or $10. A popular thing to do with these is use the part of the blade up by the handle and re-sharpen a section about 3" or 4" to be VERY sharp (like your knife would be), and then use the rest of the blade for chopping trees for shelter and the life. Also the sheaths are big and can be modified for all-in-one survival kit type thing.