Sounds like some standard maintenance. Is the bottom bracket cartridge or cup-and-cone? How good are you with a wrench?
Be careful with tires. What usually makes them roll slowly is a thick casing, not an off-road tread design. Go to a bike shop, and get a nice pliable tire. It will conform to the road better instead of resisting, resulting in reduced rolling resistance.
My mountain bike is on
these right now. They are very nice, pliable tires that roll well on and off road.
And, definitely tune that derailleur before you go buying parts for it.
Good to see a bike back on the road! I hope it all goes well for you.