Do whatever pleases you. Its just a bike, an ordinary one too. Everything about this model and value has been mentioned. With that, a quality powder coat is going to cost you. Less prep work I can get them done for $100. Then consider your time 'investment', prep, etc.. I've also painted a few with some pretty and thin laid using higher end HVLP sprayer and two part urethane. Doing it myself still has considerable cost ($75 prime, paint/reducers/hardener), not to mention the amount of prep time..... lots. When I look back, probably better to just let a pro do it and spend $300.

But.... back to your Schwinn.
If you're determined, just go for a good rattle can job. Spend time on the a very good prep, sand, scuff - DO NOT BOTHER WITH A COMPLETE STRIP - rattle can prime, sand / scuff again and rattle can spray. Get a spray can handle sprayer attachment for $3.00. The rattle cans - Rust Ole pain and primer should set you back $15. Misc. prep and supplies, $15. The quality of rattle can spray is much better than in the past. If its on your mind and disregarding and over budget project its worth the experience.