Sounds like a custom DDS type of function generator? If so, yes you need to filter (I take it you're talking about sine waves, right?), and sometimes people
use (say) third or much higher order filters.
I'm no expert on active filters, but if you used (say) passive LC types of filters then you'd need inductances of several hundred uH, so entirely feasible. There
are free tools to help you design filters. I'm sure there are free tools for active filters too.
Regarding changing amplitude, you can pick the type of filter to determine what will occur over the pass bandwidth, but sometimes signal generators
use an automatic gain control type of feature, to try to keep the signal level constant (at least for RF generators, not so sure about LF generators).
Of course, that is more work, and you may not find it worthwhile if you can calculate it, or allow the user to adjust the amplitude, etc..