Any coin collector just starting out in this hobby should begin by getting familar with the most current coins on the market. The 2008 Proof Sets produced by the U.S. Mint are a good way to start any coin collection. Proof Sets were first introduced in 1936 and continue being produced today. 1665-1967 were the only years that an actual proof set wasn't made. The proof sets prior to 1965 tend to bring more money due to the silver content.  The older proof sets pre-1950 are getting really expensive and out of the price range of most beginning collectors.
1996 Prestige Proof Set - No Box or COA (#3710)

1996 Prestige Proof Set - No Box or COA (#3710)

Price: $255.00 (3 Bids)
Act Now 15m
1983 United States Proof Set

1983 United States Proof Set

Price: $6.75 (4 Bids)
Act Now 15m
1984 United States Proof Set

1984 United States Proof Set

Price: $4.26 (4 Bids)
Act Now 16m
1984-S US PROOF SET WITH ORGINAL PACKAGE

1984-S US PROOF SET WITH ORGINAL PACKAGE

Price: $8.00 (9 Bids)
Act Now 17m
1985 United States Proof Set

1985 United States Proof Set

Price: $3.70 (5 Bids)
Act Now 17m
1982-S US PROOF SET WITH ORGINAL PACKAGE

1982-S US PROOF SET WITH ORGINAL PACKAGE

Price: $8.25 (7 Bids)
Act Now 19m
1987 United States Proof Set

1987 United States Proof Set

Price: $4.58 (7 Bids)
Act Now 20m
2009 PRESIDENT DOLLAR PROOF SET UCAMEO GEM~4 COIN SET

2009 PRESIDENT DOLLAR PROOF SET UCAMEO GEM~4 COIN SET

Price: $32.99 (0 Bids)
Act Now 20m
1988 USA proof set

1988 USA proof set

Price: $2.99 (1 Bids)
Act Now 21m
2005 S State Quarters Set Proof 5 Coins No Box or COA

2005 S State Quarters Set Proof 5 Coins  No Box or COA

Purchase Today: $6.99
Act Now 21m
2006 S State Quarters Set Proof 5 Coins No Box or COA

2006 S State Quarters Set Proof 5 Coins  No Box or COA

Purchase Today: $8.99
Act Now 21m
1988 United States Proof Set

1988 United States Proof Set

Price: $5.24 (6 Bids)
Act Now 21m

Pay particular attention to the amount of coins that were minted as well as the mint location.  Many of the highest valued coins have extremely low quantities available and are from US Mints no longer in production.  If ever in doubt about the coin your buying please contact the appropriate seller to answer any questions.  Keep in mind that condition is of upmost importance when creating your coin collection