Will these tires fit on my bike? If I were to purchase the “Aluminum Road Bike Commuter Bike Shimano 21 Speed 700c”, would I be able to remove the tires that the bike originally came with, and replace them with some “Michelin Lithium 2 Road Bike Tyres”? Links for the bike and the wheels are below. And if so, should I get the 23c or 25c? I’m riding on city streets and sidewalks.

Original bike and its tyres

New tyres on CRC website
Yes, they will fit. You should also be able to reuse the existing tubes without issue. 

As to which width tires to get, that is completely up to you. In theory, the 23mm tires will offer less rolling resistance, although in practice this may not be true. The 25mm tires will offer somewhat more grip while braking &amp; cornering.