No wrong way about it
There's not a lot of tips I can give to someone wanting to get into puzzles outside of explore what's out there. Whether it be jigsaw puzzles, sudokus or video games; there is not really a wrong way to go about it. Not all puzzles are going to be your cup of tea, though I do think everyone can find some puzzles they will enjoy.
However if I did have to recommend something it would either be some of my personal favourite games or
Last Call BBS
A game made by developer Zachtronics. If you are new to both video games and classic puzzles, this might be one to pick up first sine it combines some elements of video games with the more classic style of puzzles.
It is honestly difficult to describe what exactly this game is. It's closer to a "simulation" of a computer that holds a collection of 8 games with wildly varying visual styles (as visible on the photos page). The variety of puzzles make it a good introduction to puzzles while still having a form of cohesion and quality.