I just found a new site called Aywas. You have to send in an application to register, but that's just because they don't want a bunch of jerks/spammers/spam bots there. There are different types of pets and pets within a certain species can have different colors and styles. The colors are very pretty. There's an adventure mode, and while you only click a button, it's nice to see what you can pick up. RSing is really easy because there aren't that many users, so you have time to check how much something is selling for on the marketplace before you decide to buy it. To get new pets you either capture them in adventure mode, or they become interested in your pet and want to go home with you (also in adventure mode), or you can hatch them from eggs or buy them.
I believe they also do some kind of event every month. Right now they're doing Pride month, and they have these little items called "Pride Mochi packets" which on July 1st will become openable and you can get fauna from them. Fauna are sort of like petpets, and they can battle other fauna.
They do have premium accounts, but not to the extent that neo does, where premium has a gigantic advantage. They get new forum abilities, like signatures and being able to change their post background, access to a new game about geodes or something (which isn't enough to break the economy), and unlimited trash dumping for trash points, which you can spend at the trash shop for cool items (again, not enough to break the economy). If you buy 6 months of premium, you do get a 10% discount automatically in the shops, which adds on to the fact that you can haggle down 10% (no more though) in the shops when buying items.
They do have a premium currency, but you can get that buy selling items for the premium currency in your shop, which doesn't have an item limit so you don't have to spend any money (which is called BP, the non premium currency) to upgrade it. You don't even have to spend BP for more pet slots. They have items for that, and you can find some of them in adventure mode, so you don't really have to buy them.
You do need to pay BP to get more inventory slots, but it's really cheap, 10 BP for one slot, and money really isn't too hard to come by.