Some simple Function Generators base on the XR2206 Chip.
That offers Sine, Triangle and Rectangular functionality.
Sine has a little Spike at the top and bottom of the sine wave, at higher frequencies.
There are many solutions for that in the Internet.
The magazine ELEKTOR (
https://www.elektor.com ) bring at least 3 schematics with this Chip, last 20 years.
Pretty good Performance will give you DDS Functon Generators.
They base most on an DDS Chip and will be steered by a Microcontroller or PC.
That's a little more complex, but it bring better results and wider Frequency ranges.
This generator type make very good locking wave forms, as long, as the output frequency is quite low in comparison to the clock frequency. At higher output frequencies the dissortion will be more and more.
A good output filter is a must!
ELV (
https://www.elv.de ) has about 3 Kits for such a Generator in stock.
Most Wien Bridge Generators offers a fine Sine Wave with less distortion.
But sometimes it's not easy to stabilize that generator type for a wide frequency range.
Higher Frequency cost more Money.
Possibly a easy ready to use Function Generator is quite enough for your usage?