OP, It's great that you bought the team uniform right from the start. For those who aren't quite comfortable with the idea of cycling kit just yet, you can kind of ease into cycling clothing if you want. Start with either liner type shorts (cycling shorts with a chamois made to be worn under other clothing) or mountain bike (MTB) shorts which look like casual shorts but have a liner and chamois. Don't get the super cheap cycling shorts that you might see on Amazon or other online sources. They tend to be very thin, poorly made and of inferior materials. Most people who hated cycling shorts started out with something like that. Decent cycling shorts run from $45 to over $100. Aerotech makes some good ones (work well for me at least) in the $40-$70 range. T-shirts are OK for casual riding as long as they are a wicking performance fabric, at minimum a 70% poly/30% cotton blend. You can get decent performance Ts at any of the big box stores. They don't have to be tight but should be close fitting, not baggy.

BTW, while cycling shorts with a chamois offer good benefits, it is entirely possible to ride without them. The important thing is that whatever you wear has to be smooth with flat seams in the right places and a fast drying/wicking material. The big box stores have sports trunk performance underwear that fits the bill. I've logged many recreational miles wearing sports trunks under Wrangler hiking or cargo shorts with no problem, including some 50+ mile rides in 90F+ weather. I wouldn't recommend them for fast group rides or hard training, but if you are out logging miles for general fun and fitness, they'll suffice.

+1 on good cycling or running socks. Regular cotton socks will get wet, bunch up and cause blisters or rub your feet raw.