OP, if you're feeling self-conscious about how you look, do this --

Get a pair of bib shorts and, optionally, a base layer T-shirt (something tight like Under Armour).

Over that, wear your regular clothes, or whatever you prefer to wear at the grocery store.

Ka-ching - you get the sweat management and chafing protection of cycling clothes while looking like a regular person.

I've got my superhero poseur gear and my normal clothes that I wear for different reasons and destinations. I feel a little weird (more than usual ) going to the movies dressed like a Cat 6 domestique.