IMO, the primary and basic function generator should be analogue. Good choice would be a HP 3213 or an equivalent from Wavetek. Offers quite anything you need in a FG. I got my HP3213 for 130€ (tested, from a dealer) and if you keep your eyes open, you should be able to do as well in the U.S.
Except you decide to give the Tektronix TM500 system a chance. For all of these options, there are a lot of offers at various times. Best grabs can be done online at times when other people can't compete. Another method is to look up a serious and well stocked surplus/second-market T&M dealer and give them a visit. By doing so, you can get away with less than their official prices.
TM500 system has certain advantages for a small lab, as your mainframe can supply diverse instruments, such as Power Supplies, FG, Counter, DMM etc. Further, the modularity means that you can start with a rather cheap FG501 and replace it with a 40MHz sweeping FG504 when you need it.
Please do not listen to the voices peddling this disgusting chinese pseudo-instruments. Your T&M gear should be something you can rely on.