You don't insert the cartridges through the floorplate, you insert them through the top of the action into the magazine with the bolt open. Push each cartridge into the magazine until it clicks into place.
If you want to change your rifle over to use a detachable magazine, there are several options. The cheapest is the Remington detachable magazine, not the best magazine, but the simplest to install. Then there is QuikClip, about the same as far as difficulty of installation. Accuracy International, Surgeon, and several others make a detachable magazine for the Rem 700, but they run about $300 for the kit. With all of these, you have to replace the factory trigger guard and replace it with the appropriate trigger guard/bottom metal assembly.