Can anyone suggest some good fingerstyle acoustic guitar songs to learn?
Yes; My Grandfather’s Clock, Puff the Magic Dragon, and Freight Train.
You should be able to play all of these very fluently before tackling more advanced pieces. Watch lots of YouTube videos to see which sub-genre of fingerpicking you like. There are so many: jazz; folk; latin; blues, ragtime, etc. Find a few performers whose styles are similar and which you like. Here’s a few pros to look at: Rory Block, Tom Rush, Tommy Emmanuel, James Taylor, Chet Atkins, Tim Sparks, David Wilcox, Mississippi John Hurt, Happy Traum, etc.
A few non-celebrity players to watch on YT would be daddystovepipe, acoustictravellersl, Fretkillr. (Fretkillr does both flatpicking and fingerpicking and he is AWESOME.)
Homespuntapes.com is a good source of instruction on acoustic fingerpicking.