While it is not absolutely necessary to have a base plate and a tow bar from the same company, it does make things easier when hooking up as no additional adapters are needed.
Be prepared to spend about $3000 + labor to get all of the parts needed to tow your Fit. That is $3-400 for a baseplate, $6-900 for a tow bar, $1000 for a braking system, $250 for various wiring things. Your biggest labor costs are the baseplate installation and the wiring. You can have the work done at various place - ask your RV dealer for some recommendations.