Looking to build a custom workstation and I wanted to use something thick as my top so I thought about using a butcher block countertop from a chain store, along with an inexpensive router bit set to round the edges. Would this work?
Any common butcher block countertop can be cut and rounded to fit. You'll have to refinish the sections you've cut, but there are no other special considerations. Cheap tools are often OK for one time jobs, there are also tool libraries where you can rent or borrow better tools. Some home stores offer rentals.
For finishing butcher blocks, the traditional materials are some form of food safe oil. For a desk you have the option of sanding and using any sort of furniture finish from a wax to a varnish to polyurethane. It's best if you buy the butcher block unfinished, so you don't have to match finish. An excellent discussion (focused on food uses) is at http://www.thewoodwhisperer.com/articles/cutting-board-finish/
Jigsaw, steady hand, and sandpaper/sander. Stain it, sand it again with finer paper, repeat until you get color you want, add finish coat, sand, and so on. Remember with stain or finishing - much easier to get darker with more coats.