Any suggestions would be welcomed. Eventually I would love to be able to control it programmable
You may want to search for an AWG (Arbitrary Waveform Generator). Almost any AWG can go from 0 Hz (DC) to many MHz, which will cover the range you are interested. Siglent and Rigol are trustworthy brands yet not very expensive, and they have many models less than $1000.
Modern lab instruments (like e.g. an AWG, oscilloscope, power supply, etc.) can be controlled remotely by SCPI (Standard Commands for Programmable Instruments). Instruments marked as LXI (LAN-based eXtensions for Instrumentation) can receive commands by LAN (Local Area Network). Older/second hand would usually have GPIB (General Purpose Interface Bus) instead of LXI.
Sure you can try to build a generator in many ways. How easy/cheap/time consuming would be depends of the signal you need and the skills + time you want to put in it. If you can afford a generator, either new or second-hand, I would rather buy a generic one than one build a dedicated one.
If you define very well what signal you need, a microcontroller (or maybe just a soundcard followed by a mixer, or by a PLL (Phase-locked loop) at its output might be enough.
For the sound/ultrasound producing part, meaning amplifiers and electro-acustic transducers, that's another story. Can be many ways, you need to define what you want to achieve (put some specs and numbers), or tell what you want to study, such that people can point to relevant ways of doing that.