We were thinking tent camping in state parks. Probably get sites with electric though. We may wait until next year, taking a 3 month old might be too hard on the wife come feeding time.
My wife and three boys started off just the way you mentioned above - tent camping in state parks on electric / water sites when my twins were 8 months and my oldest was 3.
My wife bought us a "3 room" tent at Wal-mart for about $130... you can't even stay at a decent hotel for one night at that price (by the way that tent is over 5 years old and we still have it in tip-top shape). This gave us enough space to fit two pack-and-plays, a sleeping bag, and a blow up mattress for us.
Again, having water and electric at the site is great for those expected diaper blow-outs, puking, etc.
As with any activity - be it at a campsite or in a mall - parents know when their kids needs to sleep to prevent crankiness. If you stick to their normal schedules (nap, feedings, etc.), you should be fine. We never once had any extreme behaviour issues where we wanted to "pack it up for the weekend" - remember, kids will be kids and can be unpredictable any day of the week. That's why I also recommend red solo cups and a decent beer or wine for when the kids fall asleep.
With anything, the sooner you get the kids out there, the better. My boys now 5 and 8, love camping so much that we have a year round campsite at a private campground in the Poconos - we even upgraded to a 28' travel trailer.
One other piece of advice, if you are at an electric site, bring an oscillating fan. We found that by having moving air in a stuffy tent helped the kids fall asleep real fast.
I know you also mentioned "feeding time". On our second family camping trip, my wife was nursing both of the twins at the same time - she was quite skilled - when all of a sudden a big, black bear came through the edge of our campsite. Needless to say, my wife tucked both babies under her arms and was in our car in a split second. One other thing I made a habit of doing was keeping our car keys / remote fob right near the bed at night. At the same campsite a few years ago, we had a bear outside of the tent. I tried calling the ranger station, but there was no answer. Best thing I could think of was to hit the "panic button" on the car fob. The bear ran off pretty fast.