Welcome to the camping topic TheHouseofMirth, the best topic on mn
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First you need to set a budget. A budget for the tent and a budget for the rest of the clobber.
Secondly you need to decide what style of tent you want, and what fabric you want it made from. Do you want the bedrooms to be next to one another or have separate pod bedrooms? The general rule of thumb when looking is to go up bto twoto get the number of births you need, so you should look for a 6 man tent. Saying that there are 4 of us and we camp perfectly happily in a 4 man.
Tents these days are either
Polyester ( cheapest, lightest easy to dry, smallest pack size but noisy and get cold/hot depending on the weather)
Canvas (expensive, heavy, big pack size, take a bit longer to dry but quiet warm/cool and smell nice)
Or polycotton which is a polestar and canvas combo, you get a share of the best and the worst of the above.
Steel poles to support the tent are strongest but heavy.
Fibreglass poles are light but break more easily
Buying a tent is all about compromises. The other thing to think about is the bigger the tent ( and the more equipment you put in it) the longer it takes to pack, pitch, strike and unpack. How long all this takes will be a major factor on how frequently you want to go away. Believe me if it takes over a hour to get the car packed and then over an hour to put tent up you will lose a lot of enthusiasm for going away for short breaks.
There are pop up tents now that you can stand up in and are...well pop up. Not sure they have separate hanging bedrooms though.
Equipment wise IMO the best thing to invest in is what you sleep ON. Nobody loves camping if they are lying awake alnight on a cold uncomfortable bed. My vote is always self inflating mats. Look at thermarests.
Then you need something to cook on, a few bits of kitchen equipment, something to out out of and with, lighting /torches, maybe a cool box.
GOOD PEGS
and a mallet.
Sorry this is a long one. Have you seen anything you like yet. A mooch about a camping store will give you a good idea of the style of tent you like.