I cannot help you with specific places to shop. But usually there are Shop Rites, Wal-mart, Stop n Shop and local grocers in the area. For clothing you can look up your favorite stores online and do a location search. Or order right online. There is also a big outlet in Woodbury Commons to shop at they have some of your more upscale namebrands. These communities usually try to beat down strip malls and stuff so sometimes you have to look in the yellow pages then see where the store is on a map. There is also tons of shopping in Paramus NJ area off Rte 4 and rte 17.
Your definition of "country" is a little funny to someone raised in Northern OC.
The schools are pretty good and the town might not have the stores you have in Manhatten but it does have activities and opportunities you kids might not have if they lived in NYC, like hiking, horseback riding, lakes and such.
St. Anthony's is about the only thing you have as far as hospitals in Warwick. I believe there is one in Suffren NY which should not be too far. How far are you willing to drive? Within 1 hour are St Lukes Newburgh, Arden Hill, Horton (both part of Orange Regional Medical Center), Middletown NY, Westchester Regional at Valhallah (should be 1 hour or less depending on where you live in warwick), there is a psych ward somewhere around Goshen NY..there might be a few more in Northern Jersey that are less than 1 hour as well. I would advise hitting one of the online yellow pages and doing a search for hospitals within a radius. Many are online and list jobs online too. There are a couple in Sussex NJ, but it is 16 miles on back roads so I really don't know how far it would be for you. I would guess at least 32 minutes. Check out infospace.com and search for hospitals and use the "distance from address" option. Warwick's zip is 10990.