For that bike I'd look at something like these.
Microshift Shifters 3x7 Speed Road Derailleur Dual Control Levers for Shimano | eBay

For it to be a 21 speed it's a 3x7, meaning 3 chain rings in front and 7 cogs on the rear cassette. You will need a 3x7 shifters. I'm getting my specs of your bike from this link Merax Finiss Aluminum 21 Speed 700C Road Bike Racing Bicycle Shimano - Walmart.com
I use the MicroShift shifters, they are good solid components that work well. If you are wanting to upgrade I'd say start with the shifters and see how the derailleurs handle the shifting from there. No offense but that's not a bike you want to start spending a lot upgrading. Get it working well for you and if you want better plan on buying a complete better bike.