Specifications are everything, It's entirely possible to assemble a workable homebrew signal generator for ~£50 these days, it won't compete well with a HP, Aeroflex, Tek, R&S etc.etc. on the more 'finessed' specs but it will work and it will get you going, it may also be a useful learning experience.
It's possible to AM a simple sig gen, FM is a little more difficult but can be done, measuring output power is pretty simple, programmable attenuators that were intended for WiFi and Cell use are cheap and available as are wideband amplifiers, there are also I/Q modulators out there which can enable you to produce pretty much any modulation scheme you choose, it's potentially a great fun project if you know a little Arduino coding and can dedicate the time to it.
You might also want to consider that a Specan with a tracking generator can often be pressed into service as a sig gen so a Rigol 815TG or the Siglent 3021 (IIRC) might do all you need.
The 'communications testers' like the R&S CMU200 come with a sig gen built in as well as offering a decent enough spectrum analyser and other facilities that sound like they could be useful to you if you're intending to work with UHF gear in the ham bands, I have two CMU200s and paid less than £500 for the pair (possibly close to £400, I'd have to check the invoice)
There's always a decent supply of second hand sig gens for sale on eBay as well, you can occasionally get a bargain or you can buy a turkey (I paid just shy of £400 for a *very* nice sig gen that's faulty and parts are essentially unobtainable, took a chance and lost, a project that's 'on the list')