several times a month I have to do some basic teaching for friends, neighbors, and friends of friends and neighbors who bought a digital SLR and are wondering why they still can't take 'great' photos even tho they just spent $1000 on a new dSLR. Just this weekend I held an impromptu minor clinic for parents at a basketball game. Two of them had dSLRs that had never been set to anything but full automatic..... it isn't the camera, it's how you use it.
The plain truth is that for 99% of all photography, a simple point and shoot will take great pictures. Like indoor basketball, model photography is a bit more specialized and requires a few features not always found on every camera and some technique to use those features to their best. Here's what I would look for if I was going to take a lot of model photographs, and all of these are found on the better 'point and shoot' cameras:
a macro mode. This allows you to place the camera close to your subject and get at least some of it in focus. Usually this is denoted by a flower icon. You don't always need it but it is good to have when you do.
compare the minimum focus distance (mfd), less is better. Anything less than that won't be in focus no matter what settings you twiddle with. Here's where point and shoots often win, my old 1.2mpix nikon coolpix has a mfd of under 1/2", my best SLR macro lens can't focus on anything less than 12" away.
A tripod mounting hole (1/4-20). a tripod is an absolute must, even a small simple one. I have a homemade one that is simply a 1/4-20 screw attached to a t-strap bracket. It holds my SLR very stable and at only 1" above the layout.
as mentioned previously, minimum aperture is the key. In order to use it however, you need a camera that will operate in Aperture Priorioty mode, often designated as Av (Aperture Value) mode. Here you manually select the aperture value and the camera selects the rest. Portrait photographers use this to control background blur or shallow depth of field (DoF), model shooters will use it for just the opposite: to get a deep DoF so that everything is in focus. In Av, you will dial in the biggest number (f22, 32, etc) you can. If you have a choice of cameras with most other features similar, choose the one that says f3.5-f32 over the one that says f3.5-28.
Be aware that most simpler cameras will give you a smaller aperture (bigger #) when zoomed long/telephoto. It may be necessary to set you camera farther away, zoom in and then select the minimum aperture. You need to zoom in 1st as many cameras will allow you to select (as an example) f18 at a wide but you can select up to f32 at telephoto. But as mentioned, using such tiny apertures means that the shutter speed may be several seconds, making a tripod an absolute must.