We've camped with our dog before (a huge labrador) and it was great fun. We had a 2 man tent, but a biggish one so it had a separate sleeping area. The idea was to keep the dog in the 'lobby' bit while we sleep separately, which worked OK the first night, though by second night he got into the sleeping area and we didn't have the heart to move him!
Pack on the basis that everything will get wet if it rains, though it'll be as much water coming off your clothes as off the dog! Most campsites will have a hose you can use to wash the dog off if he gets muddy.
I've never yet found a campsite which allows you to leave the dog alone while you go out, and to be honest the dog would probably get quite stressed by being left alone in such as strange environment. Having said that, most campsites are in the countryside, and most country pubs are happy to take dogs, so we've never had a problem finding somewhere to eat out of an evening. Plus, if you're camping, you're not going to have the facilities to get dressed up to the nines to go anywhere posh anyway.
Day trips can be trickier. Some attractions will take dogs (eg you can take your dog into the caves at Cheddar Gorge) and others have kennels you can use while you visit (if your dog would be happy with that). A lot of National Trust type places will allow dogs in the grounds, just not in the houses or gardens.
We bought our tent new, but I can't see a problem with getting one off ebay. Just put it up in the garden when you've bought it and turn the hose on it for a bit to make sure it doesn't leak! I'd also ask around friends to see if they have a tent you can borrow to save buying one before you know whether you'll like it.
Also, consider having just one or two nights away somewhere local before you book in a long camping holiday, just to check that you enjoy it and have all the equipment you'll need (or even practice in your back garden). That way if the dog decides he hates it and howls all night you won't have lost much!
One important thing to have for the dog is a tethered rope so you can stop him wandering all over the campsite (it can also be good for keeping him away from any ground level BBQs as ours would have tried to eat the food cooking on it if he'd been able to!). We had a big metal screw thing that you screw into the ground and attached a cable to it like this one: www.amazon.co.uk/PetGear-Happy-Pet-Tie-Cable/dp/B00422L5AQ/ref=sr_1_2?ie=UTF8&qid=1437404397&sr=8-2&keywords=dog+tether - make sure you get one with a shock absorbing spring on it so if the dog sprints off it doesn't hurt too much when the cable suddenly stops him!
Alternatively, think about hiring a campervan. It's obviously a lot more expensive than a tent, but it will give you an idea of what camping would be like, but with a few more facilities than a tent. A good half way house, and if you hire one that has an awning then you have somewhere to put a muddy/wet dog until he's dried off!
Hope that helps.