The stealing kitty coins can easily be avoided. First, check the shop. If there are 0 cats in the shop, do NOT do Random, it will be wasted. If there are kitties there however, it is safe to do Random w/out losing coins for nothing.
The cats will disappear from the Shop when you get a cat from Woods or Fields (exceptions are Pretty Cat and Lil' Sprout); however, that does not mean you should not accept the cats' help, accept the cats and sell them should they prove not to be useful.
I recommend first going to Fields, and then Woods. In Fields, after you accept Sleepy (Feed will be an automatic win), sell him/her for 2 Coins. Although Think is useful, you simply need to check the Wholesome Cats Fandom Wiki to guide you through (I take credit for editing and adding things and I am not very humble). Then it should be Meeting Leaf. After Meeting Leaf, that's when you try and get all the cats you want. At the very least, get all the cats before you meet sweet and cute uwu. You might get a Ghost Cat in the level before, but I assure you they are not very useful. Sell them for 1 Coin.
Accept uwu, and do NOT sell her--Love is very useful and Princess Leaf is the only another cat who has it. I do not sell uwu, she is too sweet to be sold (I swear she's so cute).
Hope this helped!
Ηοπε τηισ ηελπεδ!