For any given player, a well-known autographed card from a popular set could be worth hundreds or even thousands of dollars. The key factors that affect the value of such a card are the player's popularity, the desirability of the set, and how well the autograph is preserved.
To start, let's look at some general guidelines for what an autographed card from a popular set might be worth. Generally speaking, if the player is still active and has maintained a good public image, their cards will be worth more than players who are no longer active or whose public images have been tarnished. Similarly, cards from sets that are highly sought-after by collectors will also fetch higher prices than those from less desirable sets. Finally, cards in better condition will always be worth more than those in worse condition - even if they're from less popular players or sets.
Now let's take a look at some specific examples. One of the most valuable autographed cards ever sold was Mickey Mantle's 1952 Topps rookie card, which went for $564,000 at auction in 2016. This card is valuable for several reasons: Mantle is considered one of the greatest baseball players of all time; his 1952 Topps rookie card is one of the most iconic and sought-after cards in existence; and finally, this particular example was graded as being in near-mint condition - meaning it's about as close to perfect as you can get.
On the other hand, an autographed card from a less popular player or set might only be worth a few hundred dollars - even if it's in pristine condition. So it really depends on who the player is and which set their card comes from. However, if you have an autographed card from a popular player or set that's in good condition, it's definitely worth getting it appraised to see how much it might be worth!