I wear running shoes and don't have a problem, but I've never tried cycling specific shoes so I don't know if I would be more comfortable in them or perform better. I'm happy enough with what I've got so don't see any need to change. I suspect that as you cycle more you'll get a better idea if you're likely to suffer any foot pain or other problems because of your shoes.

As for the jersey, I don't think it's absolutely necessary, but I've become a big fan of using good materials for any clothes I exercise in. Cotton t-shirts are hot and sweaty when you're working out. Even an inexpensive "activewear" shirt like this will go a long way to keeping you comfortable. Oh, look, they even have a bike version of the shirt here! No idea if it's any good, but I have one of the former shirts and it's comfortable. I've also found that close cut shirts are pretty flattering because they don't bunch up and cling in odd places.

Sarah