Realistically, it will depend on several issues. Male or female, age / size. Also, post apocalyptic your going to have issues with ammunition.
Handgun I'd say a Glock 17, 9mm. They are durable, have a high capacity magazine (17 rounds) and the ammo is plentiful.
Rifle I would say either an AR-15 (civilian version of the M-16). It's a .223 round (again plentiful ammo) and will get the job done. Plus it's military so finding parts, magazines will be easier. An alternate would be an AK-47, maybe not the greatest long range accuracy, but it's even more plentiful in terms of parts, ammo (7.62 x 39) overall ruggedness.
Firearms general vary by agency. i.e. Secret Service carries a Sig Sauer P229 (.357 Sig) while I believe the FBI currently carries a Glock Model 22 (.40). As CIA agents actually try to avoid "issues" I think the use of a regular firearm would not be prudent, so they probably adjust it to a need specific case.
Partially correct. There are magazines and clips. Think of it this way. Magazines hold the cartridges and have their own feeding device that helps load the next round into chamber. Clips hold the ammo in place, without a feeding mechanism, and the gun does the work of chambering the cartridge.
Technically the speed loader you showed is a completely different animal in that it only loads the gun and then is discarded.