1. Wash the entire trike with soap and warm water. I would use Dawn detergent to remove any grease.
2. Allow the trike to dry in the sun and/or towel dry it.
3. Use a metal brush to remove the bulk of the rust and then I would sand the entire trike with a fine grit sand paper to smooth and to degloss the surface.
4. Wash the entire trike again to remove any dust.
5. Tape off the wheels and any other features I would not want paint on. The wheels could be covered by a plastic bag and then taped in place to use less tape.
6. Use a rope to hang the trike by a wheel rod or some other taped feature. The rope will allow you to string the trike from a tree branch or something similar and also to move around the trike while painting. I would try to find a location which is open so you don’t have to worry about ventilation.
7. Now it is ready to be painted. I would use spray paint since the curves and uneven surfaces would be a touch of a nightmare to hand paint smoothly and evenly in my opinion. Use several light, sweeping coats for the best finish. I would look for a metal paint preferably a primer/paint combination to save my efforts.
I don't think that's too much work but then again we like refinishing pieces for a second or third go. We find these projects fun. In terms of cost if you don’t have the materials (wire brush, sand paper, tape, paint), then there won’t be much of a cost savings as compared to buying a new trike. The project could easily be tackled in one day. There will parts of the project where it sits to dry so it won't be too bad overall. Good luck.