Hi there reptile and welcome to the forums!
1) I'd work out your filter situation first, as you want to get the right before you start your fishless cycle. You could get in a discussion here on TFF, both here in beginners, or perhaps also over in the hardware section if need be. You'll want to understand the principles of mechanical, chemical and bio filtration and make sure any filter you get is ready to be a good mechanical and biofilter and that it will have the flow rate for the fish stocking level you intend.
2) Although both the Add Daily and Add & Wait methods are outlined, in my experience most of us here follow the Add and Wait method of Fishless Cycling. Its important to be active in your questions here in your beginners thread as the outline doesn't necessarily cover all the questions you'll have. But again, if you can stand the delay, you'll be better off having worked out a really good filter before you actually start your cycling.
3) Fishless Cycling takes between 3 weeks and 3 months depending on your situation and luck. If you are able to find access to some mature media (the name we give to a bit of sponge or other media from someone's old filter) you can sometimes speed up things a bit but that too is unpredictable.
4) You've already had a taste of a filter where the manufacturer is reducing the flexibility to you, the consumer, in an attempt to encourage a steady revenue stream from you thinking you have to buy replacement "cartridges" or new media. Neither of these things (cartridges or regular media replacement) is actually needed if you know what you are doing as an aquarist. The best filters (large ones with open areas or trays where you can put your own choice of media) to not limit you and the best types of biomedia (ceramic rings, ceramic pebbles, sponge etc.) need very little or no replacing over a lifetime.
The members here are great and no doubt will give you lots of help with filter specifics and then with getting your fishless cycle started after that. Then you'll have weeks during which you can discuss how to transition to having fish and what the initial fish should be to start off the growth of your aquarium population. Good Luck!
~~waterdrop~~