Bandwidth, functions (types of signals generated), one vs. two channels, and accuracy might be some of the key considerations along with the budget. If possible, try to anticipate what you are most likely to do with the signals you generate, and how much bandwidth you will need to do that.
Another consideration is what you will use to measure or observe the signals. Awhile back you were inquiring about oscilloscopes - did you select an oscilloscope or do you have one in mind? Function generators can help you learn and do stuff, but they often work in concert with an oscilloscope (not always, but often).
A kit might help you learn how a function generator is designed; an off the shelf assembled generator might give you somewhat more performance. It kind of depends on whether you prefer to learn by building (and then use the completed kit to support other projects) or whether you prefer to learn (and further build) by using off the shelf assembled equipment. Either way, it might be good to think about how the generator will be used with the projects you anticipate and how it will work alongside other test equipment that will go on your bench and that will need to fit within your overall budget.
Sometimes it's hard to know what you will do with test equipment until you have it on your bench. If it's too difficult to anticipate where all this is going, I'd get a $9.99 XR2206 generator kit, have fun building it, and then see if it has any limitations as you use it for experiments and projects. If it doesn't have any limitations, you are all set. If it does have some limitations you will know what they are and this knowledge will help you select your next generator. If on the other hand you can forecast your bandwidth and other likely needs, then spec out what you need and look for the best bang for the buck that will meet those specs.
My guess is the first thing you will miss with the XR2206 is a BNC output, so you could skip the XR2066 and start with something like the ~$33 FG-100 DDS. Probably the first thing you might miss with that is more bandwidth, so the next stop is probably something approaching or a little over $100 like a FY6900 or a UTG932. Somewhere around there I'd be holding out for two channels because there is nothing like comparing two signals side by side when it comes to testing and learning.
Enjoy the journey, a generator can be an excellent tool for testing, learning, building, and repairing.