If you have the budget you could rebuild the engine and spend as much money doing it as you have budgeted and there is nothing wrong with that.
Or it would be real easy to get running right and be fun to drive in the mean time. Is the engine healthy, compression wise? You can really do a lot with a 350.
My Camaro had the same thing, basically a stock 350 that had been sourced from a truck based on numbers, I spent some time getting it to run right, just tuning is all it took, and drove it quite awhile and at the same time I worked on building the first motor for it, a 406. Then you can swap the motor over a weekend and be driving it again in no time.
It really depends on you, some guys are ok with stripping the car to it's bare bones and starting a full restoration, that takes time and money but thats what some guys enjoy.
To me, I like to drive the car and enjoy it, while doing projects on it keeping the down time to a few weeks so I can be back driving it (except this last one has had me down for two years....
). It's all about driving and enjoying the car to me, some guys enjoy the build and sell when done.
Either way set a realistic goal and enjoy the process!