In my experience on the cheap isn't the best way to build one of these. If you go the cheapest route here is what you can expect:
Cheap printed parts - I have found that people who are selling parts the cheapest don't spend too much time inspecting them. If they are warped or deficient in some way you might be lucky to still be able to make them work until you can print a replacement, but then you have to take that beautiful printer back apart again. Also the cheaper sellers might not have a very well tuned printer and the parts may not look that good and even have dimensional errors. Don't by parts unless the seller has a really close up pic of them. All of the lines from printing shouldn't be wavy and should line up on on top of another. Verify where their model files for the parts came from. I would recommend buying parts printed directly from that printers source files unless you really research and know what ever modified version your supplier used is really what you want/need. These are the foundation of your printer mess around as your printer needs to be square and true to print nice parts.
Cheap hot end - Those do it yourself and assembled from a kit using a PTFE (Teflon) tubes are a joke. They are hard to assemble and even when done right still have issues that will give bad prints. By the time you mess around with one of them you would have been better off just saving a few more buck and buying a jhead.
Cheap motors - I've got cheap motors on mine and they work. However, some people have some with step angles that aren't fine enough and or voltage requirements that aren't correct for the reprap setup and therefore run too hot causing various printing issues (like missed steps).
Cheap power supplies - Cheap PSUs will over promise and under deliver. Under full load of all the electronics and the heated be they will drop too much voltage. These printers run off of micro stepping motor drivers that rely on precise current values to move the motor a partial step. When the voltage is off the current is going to be off too and therefore you step isn't going to be for the correct distance resulting in errors in your print.
Cheap rods and bearings - Cheap smooth rods won't be of a uniform diameter and depending on your bearings can cause binding. Of course, if you have cheep bearings too, they probably aren't to size either and will either result in too much play or feed into the binding issue.
I'm not saying you have to buy the highest priced parts out there. I'm saying don't buy the cheapest ones. Buy rods that were meant for linear motion, there are some that are hardened and chrome plated that are just under double the cost of cheap rolled tool steel rods. Things like that. Spend a lot of time shopping around for prices. I wouldn't spend less than $800 USD on a printer.