I go hiking and wild camping a lot. Generally people fall into two categories as with most outdoor activities and they either hate it or love it.
My advice would be not to rush out and buy loads of expensive gear straight away in case you don't enjoy it. Not everyone does.
Borrow some kit from a friend if you can, or if not, Decathlon is a great starting point. They do some excellent hiking and camping gear and very affordable prices.
And *DO NOT TAKE THE MRS*. Trust me, if you get into it, it's a brilliant opportunity to get away for a bit and have some peace and quiet.
I don't have a dog but loads of people take their dogs hiking and camping and dog's generally absolutely love it.
As for campsites, the one at Edale in the Peak District is great for exploring the Kinder Scout area and there's tons in the Lakes. There are campsites with basic facilities at Wasdale Head and Seathwate Farm in the western lakes which are great for the Scafell range, or Glenridding / Patterdale for the Helvellyn range. Really too many to mention but those are just off the top of my head.
I don't stay in campsites but those are all well liked places that are also very cheap and a good starting point.
Check out Paul Messner on YouTube, he has some excellent videos for people new to hiking and camping/backpacking.
Like many other hobbies though, if you do get into it it'll drain you of all your money. I spent 700 quid on a Hilleberg one man tent recently, which to most sane people will sound obscene I know.