I have a tape deck only HU. I was going to put new speakers into my truck but I am wondering if I will have to buy a new headunit? I mostly listen to radio but occasionally will listen to a CD, so a CD player isn't a must. Will new speakers with my stock HU work?

2001 Extended Cab

 

They most certainly will. Of course you will get tons of opinions on what the best speakers are. The best thing is to go to a few audio shops and listen to differents brands with the type of music you listen to. Even better if you have some friends with F-150's that have different brands of speakers that you can demo with. That would give you an even better idea of the sound.
Good Luck