The main advantage of the Woodchuck for me is that it is easier to keep the tapers straight. With hand tools, it's easy to get started wrong, and a crooked taper is an abomination! It literally ruins the arrow, unless you have enough length to cut it off and start over. I always do the nock taper first, for that reason. It's the most critical of the two. If the point taper is a bit off, field points may still shoot well, but you can't use the shaft with a broadhead. Many, if not most wood arrow "fliers" are the result of tapers that are not perfect.
Since the Woodchuck is not in your budget, go with either one of the better hand tools. The cheap little grade-school pencil sharpener types are about worthless, IMO. The most important part of using the hand tool is to start with very light pressure until you're sure that the taper is going to be straight. I make sure that the end of the shaft is cut perfectly square before starting, to improve the odds of getting it right.