That's quite a project for someone who is new to bikes. Also, likely to cost more than the bike is worth just for the conversion parts.
Brake levers: Road brakes, whether centerpull or sidepull, will require cantilever levers. As compared to most modern V-Brake levers, canti levers pull less cable. If you use V-Brake levers, you will find that you don't have enough 'oomph' to fully activate the brakes because of the lost leverage. The good news is, while a bit harder to find, canti levers tend to be inexpensive. Brand doesn't matter.
Shifters: Your choices are Grip Shift or trigger shifters. Are your current gears indexed (discrete clicks between each gear?) If it's not and you want indexing, you *may* have to buy a new derailleur too, as an old derailleur may not require the right amount of cable pull to work with indexing systems. Count the number of gears on the rear wheel, whether it's a freewheel or a freehub/cassette doesn't matter so much. Your shifters need to match the number of gears. One thing to look out for - SRAM makes two lines of shifters/derailleurs. Their ESP line-up is compatible only with itself. They also have Shimano-compatible gears and shifters.