Reddit reviews Geometric Puzzle Design

I only want to add a few things to this excellent answer: This book by Steward Coffin is another one I like to recommend. There is also this one you can read online for free.
I do also recommend starting out with a simple burr puzzles, for example with one of the classical 6 piece burr puzzles. If you find good square stock you can get a long way with a good hand saw and a chisel - but if you have access to a table saw even better:)

Then also consider the difficulty: There is the level (a sequence of numbers that tells you how many moves you need to remove the n-th piece) as well as the fraction of valid assemblies / total number of assemblies, that tells you how many configuration of pieces that could theoretically form the desired shape are actually physically possible. In the case you're new to woodworking I recommend starting out with a puzzle that is easy to manufacture. The ones without any internal edges and corners are sometimes labelled as "notchable", which means that they can be made using only straight cuts. (There is also "millable" which relaxes this condition to allow for internal edges.)

Lastly I recommend the "burrtools" software, as you probably need to try to assemble the puzzle a few times to check for tolerances etc: It is made for computing solutions to burr puzzles - but it takes a while to understand how to use (there are great instructions though) - if you need any help with this or just want a finished file for a specific puzzle just ask!

And finally: Don't forget to post your progress/result here :)