I'm not sure what you mean by your feet felt close to the bike: were you hitting anything with your feet - like the chainstay or the cranks? If not, then my suggestion would be to continue riding as they are until you have some miles - then see if they still feel too close to the bike.
Your hands probably hurt because they aren't used to riding, but you do want to make sure you aren't resting your weight on your hands. As with anything new you'll toughen your hands up some the more you ride but your hands, arms, and/or shoulders should never be painful. If they are, you need to be sure and transfer your weight to your sit bones and off your hands.
Cadence: it's not unrealistic to have a 90 cadence your first time out, cadence is how fast you're spinning your feet, not necessarily how fast you're going.....so yes you could be spinning a 90 cadence. If you aren't and it's only your first time out, dont' stress it. As you get used to the bike things will come easier.
Congrats on your first ride tho - isn't there something about being on a bike that is just uplifting and free-ing and relaxing all at the same time.
I loved the line I read somewhere about
a bike is the only vehicle whos passenger is also it's engine!
Enjoy!
Life should NOT be a journey to the grave with the intention of arriving safely in an attractive and well preserved body, but rather to skid in sideways, champagne in one hand, strawberries in the other, body thoroughly used up, totally worn out and screaming: "Yeah Baby! What a Ride!"