Today's main cryptic (the one you've linked to) was unusually hard to get in to, I thought - not a good one for a beginner!
Monday usually brings a puzzle by Rufus, who is generally easier, though some of his "cryptic definitions" can be a bit "off-the-wall".
There is a library of puzzles available from here
https://www.theguardian.com/crosswords
so you can pick and choose.