I would stay away from painting unless it is really in a bad shape. As for spray can painting it can be done poorly or decently good depending on your skills. I would advice doing practice runs on something similar in texture, but disposable. First scuff up the surface you are painting with something like 600 grit sand paper and clean the surface with grease remvoer. Then use primer meant for plastics for example automotive spray paint meant for plastic bumpers etc. and warm up the can and mix well before starting to apply. Apply several light coats with decent time between them (follow instructions on the paint can) and once you are done let it cure for a day. Then use something like 1200 grit sand paper to wet sand the primer to smooth finish. Clean out lightly and then apply your color with even coats and some time between each coat. Finally we do the same with clear coat. Choose your preferred clear coat be that matt finish or with shine. Then apply it with same principle as the base color, but be careful at this stage especially not to get runs or all your hard work will be undone. Also several layers of clearcoat can hide some of the issues with base paint coat, but it doesn't get rid off them completely.
If you are unsatisfied with your test piece or feel like the finish isn't what you hoped then I would advice turning to a professional for the paintjob. Removing parts you don't want painted, prepping finish by removing any grease and scuffing up the surface can lower the price of the paint job since your painter doesn't have to do the prep work.