Grading Mint Set?

Mint sets as a whole are generally not graded since you can have a wide variation of grades between the coins. Some people will cherrypick mint sets and break up the set selling off the low grade coins and keeping the high ones.

In most cases, high grade MS coins will be worth more than a proof. MS65 Franklins(especially those with FBLs) are not common but high grade proofs are relatively easy to find since they were made specifically for collectors and enclosed in special packaging to protect them thus giving them a high survival rate. Most proof Franklins will be PR65+ whereas most uncirculated Franklins will be in the MS60-63 range- it is all about conditional rarity.

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Example: In using the Red Book, the values of half dollars are listed as MS-63 Choice Uncirculated, MS-65 Gem Uncirculated and PF-65 Gem Proof. So a mint set's half dollar could be any of these grades?

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If the half dollar came from a mint set, it could not possibly be proof since proof is a type of minting, not a condition. Until recently, coins in mint sets were no different than the coins placed into general circulation. Proof coins are minted from specially prepared dies and planchets and are generally double of triple struck to produce a high level of detail.

Two bell lines low and three lines above them. The lines must be fully separated and cannot be broken i.e. a ding from another coin.