I have owned a 36 Ford 5WC since 1960 and know a little about them. Sounds as if you have a great car to start from. Definitely street rod it. Mine had a flat head in it until 1996 and was fairly original except for wiring and hydraulic brakes. Very limited for driving pleasure. It now has a Fatmans stage III front suspension, a 57 Chevy rear end with Mustang II leaf springs, a 300 HP 327 Vette motor, and a 700R4. The frame has been boxed in the right places and the X member modified slightly (I still have to pull the front end and motor to change out the tranny). Outward appearance is stock except for the wheels and the tail lights (I removed 1.5" from them to make them shorter). The instruments and steering column are original and working as well as the inside door handles and window cranks. The wiring is Ron Francis and I use his computer to control the lockup functions of the 700R 4. I have about 30,000 miles on it since finishing in 99.
If I were doing this again, I would buy a rolling frame from one of the many vendors offering them. It would have a Mustang II kit and either a triangulated 4 bar or 4 bar with panhard bar in the rear. I would look at air suspension but probably stay with coil overs front and rear. For a cruiser car, I would stay away from a Ford 9" rear end because it eats up some horse power over a GM type. I like the 55-64 Chevy/Pontiac rearends because of the track with works and they are tough enough to handle up to 450 HP. In the long term, if you value your labor, you will have a better frame with all new stuff as cheap as you can upgrade your frame. In fact it may be cheaper if you sell your rolling frame to someone restoring a 36 Ford.
Put what ever motor you want in it, but if you use a SBF, it is going to eat up about 2.5 inches of your interior vice a SBC. Either way, I would come into the 21 century and make sure I had EFI. A 5.0 HO Ford or a LS1 or LS4 or the newer 5.4 GM all make for a smooth running, no leaking, peppy, and fuel efficient set up.
There are a lot of little things to consider in your build so when you have questions, fire me a PM and I'll be glad to offer my thoughts. I also can steer you toward lots of repro parts vendors that can handle your needs.