FWIW I found Bob Atkins' site helpful when I was hunting around for a new kit a few years back. Good forum with good advice. In general, unless you are hardcore, the recommendation was to go with a consumer/prosumer body and spend your money on your lenses. I bought a 40D new, then a few months later I added a used 20D backup body from Adorama. It was the first used camera body I had ever purchased and I was nervous, but the transaction was smooth and I was pleased with the product. I saved a good bit of money buying used, and I had two camera bodies to work with which allows me to "switch" lenses without changing them out (a life saver if you ever have to send a body in for service). So I opted for cheaper bodies to focus on building out the lenses in my kit.
I find primes to be a joy to work with, producing incredible images and often without the need for a flash. I've got an assortment of primes; for frogs I mostly use my 100 mm 2.8 Canon macro. It's generally not fast enough for unassisted photos, but when properly lit with either a flash or additional lighting it can produce stunning images. Outdoors, no other lens in my kit can approach its sharpness. I also have a 50mm 1.8 and an 80 mm 1.8, and they produce awesome images indoors with no flash. I'd say 60% of the kid pictures are taken with the 80 mm. Outdoors, I use a 28-135 and a 70-300.
As you can see I'm into Canon, but you cannot go wrong with Nikon either. Pick a vendor and realize you will be a Canon or Nikon person for the rest of your life once you buy into their lenses

I'd say find out what your friends have, then buy that body so you can share lenses. The other thing you can do is find a local shop and rent a lens for a weekend to get a feel for it - nice way to try something out before investing.
One item you should consider is a good tripod. It's pretty valuable working with frogs. I like a heavier tripod - I trashed a 28-135 lens when my old cheapo tripod tipped over. I replaced the lens, but then I dropped some coin on a manfratto with a pistol grip and a Canon remote trigger. That combined with the 100 mm 2.8 macro is the mainstay of my frog kit
I don't think you would be able to pull all that off for $1K, unless you go used on the body (maybe save $200, but you'll give up the kit lens and trade for a better body). The 100 mm 2.8 (non-IS) is about $550, a new T3 with a kit lens is around $500, and $300 for a good tripod (base with pistol grip) would put you at $1350 or so. That would give you a walking around lens and a frog lens. I use a CHEAP (seriously - $30) ring lamp for macro work, so that would help with lighting. Anyhow, that blows your $1K budget a bit, but you could look used to knock it back closer to your range. Generally once you buy high end consumer (or dare you stray into the Canon "L" series professional lenses) lenses you will have them for a LOOONG time. I got into SLR 20 years ago and never looked back.
All the SLR's have a "full auto" setting that you can use as a beginner. As you get comfortable with the camera you can start experimenting with different settings. There's a good series of books by Scott Kelby that introduce you to digital photography. They are cheap too - I think I paid < $15 for mine.
Good luck!