I would start with the Cyfres Amdani, level Mynediad. They’re books specifically designed for learners.
You might also like the magazine Lingo Newydd, which you can also read via an app. It’s for learners and has content in three levels, so as you progress you can go back and read the more complex versions of articles.
Re bookshops, I love cantamil.com and Palas Print. Both are very helpful and will talk to you in English or Welsh. You can of course also buy from Amazon, but I prefer to support independent Welsh bookshops as they contribute to the economy and therefore sustain the language financially, where Amazon often removes Welsh language book reviews for “breaching content guidelines”!
To your question about written Welsh, yes it does vary. Written Welsh varies a lot more than you will be used to from standardised majority languages like English, Spanish or German. Aside from the differences you learn early on, fiction often represents spoken norms when presenting dialogue or internal narrative, and non-fiction often uses literary forms that are only used in writing.
However if you stick with content for beginners you’ll be fine as it’s deliberately graded to keep it accessible, and by the time you run out of that you’ll be able to cope with the variation. My tip is to say the words in your head. 1) that forces you to absorb instead of translating and 2) saying the words helps you see through variant spellings to words you recognise. Also, saying the words helps you appreciate the use of language.
Have fun pob lwc!