Are you ok with co-sleeping with the kids?
If so, I'd honestly start with a smallish family size tent.
We have a vango ventura 500 and love it. It is big enough for 2 x double airbeds which is enough space for us all. It fits easily in the car and is up in 10 minutes. It cost about £85 iirc, 4 years ago.
However we've also camped in much smaller tents. Will you all fit in a normal sized double? (We did when there were only 4 of us). If so, get a tent big enough to take a double airbed!
Airbeds: Personally I'd go for comfort for everyone, aside from anything else, if the kids don't sleep well, you won't either! Until last year we were all on double airbeds.
We also take mats for under the beds (insulation), 3 season sleeping bags, and as many duvets and pillows as we can fit in the car.
We don't do big tents, they are just a faff and imo unecessary with little kids. You will want to either spend all day outdoors (if it is sunny) or tbh go home, or at least somewhere dry, if it is wet. You can't keep 2 x toddlers in a wet tent for a day, really not, and anyway what would be the point?
Oh and don't plan to cook, (maybe tea/coffee) on your first few trips, there is something really stressful about outdoor cooking with little kids around, plus there is then washing up which is too faffy. Do cold food/takeouts and work up to the cooking!
I do think camping with toddlers is a lot of fun and they love. Just keep it simple!