If your budget is 2000 dollars, you can get a very nice camera. Don't be tempted to splurge everything on the latest and greatest body, invest in glass.
I'm a Nikon guy, so I'll take care of the Nikon side of things:
Nikon D3100 - looks like a great body so far
Your budget allows you to get a small step-up as far as the walkaround lens goes, so I'd skip the often bundled 18-55 VR, and go for something like the 18-105 VR, which gives you a bit more range.
Also, I'd get a nice lens for low light situations. Nikon's 35mm F/1.8 is a quite popular lens, and it works very well (I have one and like it).
I doubt Nikon will announce anything groundbreaking in the mean time, so you might as well buy now, and familiarize yourself with the camera and lenses.
However, you also mentioned your kids play cricket, which would mean you need quite a tele zoom. Normally, for budget DSLR users I'd recommend a cheap sigma 70-300mm lens, but optically it's....not the best in it's league. With your budget, you should be able to stretch to a 55-200 VR, 55-300 VR, or a 70-300 VR.
I assume cricket is played outside, and often in good conditions, so the stabilisation will not be too much of a benefit, but all of the lenses I mentioned should be sharper than the Sigma. Right now, I'd say the 55-300 is the best option.
Despite what you might think, a tripod is not really neccesary anymore, especially for outdoor sports. Current technology allows you to gather more light, and allows you to shoot at higher shutter speeds to freeze your subjects. It also has the added benefit that camera shake is mostly eliminated at high speeds. I wouldn't recommend a cheap tripod for sports anyway, unless you love pieces of equipment that don't do what you want.
A monopod, however, could be something to consider. Not really for the stabilisation, but for the weight. Not knowing your physique, standing alongside a game with camera and lens can be somewhat fatigueing for your arms. It also gives you more freedom than a tripod.
I myself use a monopod sometimes for sports for that exact reason (but I have what some people call a monster lens) :p