Entry level dSLR for low light/action?

I'm looking to get a dSLR that would take action shots in low light-- kids playing indoor soccer, swim meets (indoor pool), basketball games, etc. Of course, I'd use it for other situations as well, but right now, my focus is low light/action.
I currently have the Sony HX1. Which is fine for outside, everyday kind of situations- kids at the park, etc.; but it takes less than optimal low light action shots.
I'd like a camera that would grow with me as I learn about ISO, aperture, etc-- but not one that's got a HUGE learning curve- so much that I'd never figure it out.

There are a lot of options and opinions out there-
I've read that for low light/action shots, it's all about the lens and that the camera body doesn't really matter. Conversely, I've read that both are equally important.

Am I best to buy a "kit" with the camera body and a couple of lenses to start out with?
Realistically- which lenses should I be looking for, considering my main objective?

I'm not necessarily looking to buy the cheapest thing out there, as I know a good camera- one that will meet my current needs and yet grow with me, won't come "cheap". Nor do I want to have to get a 2nd mortgage in order to buy a camera that will take the pics I want to take.

Can I get it all for less than $750? Good camera, a couple of lenses, case, etc?

Are there accessories you would consider NOT optional?

I've looked at the Nikon D3100. The Canon T1i and T2i… As well as the Pentax K-x and K-r. And I'm at a loss. Oh- and HD video isn't a big deal. I don't know that I'd use it.

Any DSLR will work for low light action shots as long as you also purchase a fast lens like a 50mm f/1.4 or 85mm f/1.8.

You'd need to stretch your budget a lot if you're looking to get some good lenses too… Lenses are very expensive and you don't want to waste your money on the bad quality ones.
I'd recommend a Nikon D3100 or the Canon Rebel T2i, to decide between them you'll have to go to a camera shop to try them out and see what they're like. I'd recommend the Canon just because that's the brand I know and use but Nikon make cameras that are just as good and even better at times.

To go with the camera you'll want fast lenses, these are lenses with very wide apertures, or low F numbers such as F2.8, F1.8, F1.4 etc. Try not to go below F2.8 if you can.
I'd recommend something like a 50mm F1.4 or F1.8 and an 85mm F1.8. The Canon 50mm F1.8 is excellent and it's only about $100.
Zoom lenses with wide apertures will cost you a lot of money as will wider angle lenses.
But it's something you can save up for over time. A good bag is important too. Get something that's weather proof and big enough to let you grow into it so it will be with you for a good long time.

Pentax Kx. At ISO 12800, you can pictures in the very low light. Be warned that anything shot above ISO 400 would be too grainy for anyone's comfort.

If you want good one for low light Canon T2i is a great choice with ISO 100-6400.

Main question here is…

Are you someone who sees yourself as a photographer? [oriented to the process, the results, AND the creative process connecting them]

Or are you someone who wants to be able to get good-quality pictures of family and friends, when you need something to capture an event or a happening? [oriented primarily to the good-quality pictures]

The difference being… A photographer practically has a relationship with both the camera and what she/he is shooting.

The picture-taker wants a nice result, but isn't necessarily looking to make a production out of it, or to be thinking, how can I make this better, more sparkling each time I do it.

If you are an aspiring photographer, I would advise to consider the Nikon D90, Canon 40D or 50D, or Canon T2i. Those cameras will be more adept at becoming an extension of your mind and hand, over time.

If you want nice results but not so much thinking of yourself as a photographer, I would say chances are you will be fine with the Nikon D3100 or the Canon XS or XSi [no video], or Canon T1i, or Canon T3, and you can save some money.

NOTE: An earnest photographer can do great and amazing things with any of these, so if money dictates your choice, don't worry about it, just shoot and keep shooting. You could even get an inexpensive Nikon D40x [older but it will easily eclipse your compact Sony] and put the money saved into lens(es).

As to the lens(es), I'll let someone else respond to that part.