There are so many brands coming out of China its hard to know. You'd have to test each to know it delivers as specified.
If you are looking for low cost function generators and know what higher end frequency you want, I would look at B&K Precision's equipment line.
Its no frills when it comes to the case and external parts, but they are electronically sound, and if you are in the USA, its easy to return it if you're not satisfied. As a company, they've been around for over 30 years, so they must be doing something right and they are still the same company, not bought out.
The key feature in function generator performance is distortion free wave forms and frequency stability. If you select sine wave at 1MHz you want to get 1MHz and you do not want it generated with distortion, thats a basic test, and you don't want the frequency drifting up and down either. If you read the spec sheet, the device should truly deliver those specifications to you. B&K is a popular FG maker because most low end designs work well with their product line.
Switch the FG to square wave, and retest. If it delivers a good square wave, then you're good to go. Any distortion in a square wave reflects poor frequency response.
The next item is about shielding and safety. If the unit is t shielded well, or your probes bad, the high frequency waveforms will be distorted, and it won't be the fault of the FG. You also need a good scope to read those waveforms without distortion.
http://www.bkprecision.com/generator-guideFor most at home design work something like this is all you need:
http://www.bkprecision.com/products/model/4001A/4-mhz-sweep-function-generator-with-dial.html
Or the next model up, the 4003A.
Once you start working on RF frequency designs, you start to get a bunch of problems with shielding, drift, and board layout. So you need to prototype it on design software really well before building it. If you make it that far, you should jump up to a professional grade FG by Agilent or others.
If you can find a DDS based FG that >= features/cost as the low end 4001 B&K [~$US 200], such as the those Chinese branded FGs [$190 pictured below], its a better deal, but I don't know how well they'll live up to their spec or their warranty.

Its a matter of trust, unless someone reviews their models like our hero, Dave!