Tough choice between a spreader and a sprayer - I'd have to say we use ours about equally. Not only can you use the sprayer for herbicide application, we also use ours when we're burning plots and fields.
If I had to choose, I'd probably go with the spreader though, spreading fertilizer and lime through a hand spreader would be a big chore. The hang off the back spreaders you can get for about $80, only problem is they rely on gravity to send seed to the spinner and don't have an internal agitator to keep things from clumping. They do work well for small in the woods plots though. The tow behind spreaders should have an agitator inside to keep things from clogging the drop holes, but found that in tight areas turning created problems. We had a cheap tow behind, but it didn't last long - if you get one, don't cheap out, spend the $$$ and get something that will last. No matter what type of spreader you get, wash it well after each use, fertilizer and lime are deadly to metal parts.
“There are two spiritual dangers in not owning a farm. One is the danger of supposing that breakfast comes from the grocery, and the other that heat comes from the furnace.”