Generally ALL compacts have video mode now.
Very few D-SLR cameras have video mode. The photos will be noticeably better on a D-SLR and the price of an entry level D-SLR...like the Nikon D40.... is not much more than a higher end compact,

DGIC (DiGital Imaging Core) sometimes called DiG!C, is a type of processor found in some Canon digital cameras. It has gone through several versions. DGIC, I, II III, 4, DV, DV I, DV II.

If you are planning to take just portrait photos at the start you have many options. Doing event photography such as sports or performance (bands, dances...ect.) you would need a camera with a fast burst mode (continuous shooting). That is what some of the cost of the more expensive cameras is for.
Some good cameras to look at as portrait cameras are:
Sony a300
Canon Xs
Nikon D60

As for the printer...if you are going to print just 4x6 prints (which I would suggest) look at the Epson
Picture Mate found here: http://www.bestbuy.com/site/olspage...
It has a built in card reader and screen so you don't have to use your camera as a pictbridge.
Printing a 4x6 on the spot is great and if your customers want bigger prints they can order them and you can print them out at home later. People at parties don't usually plan on carrying a 8x10 photo around with them.

There are a few other things. The Auto Focus goes to 9 points vs 7 points on the sx. This will give you more focus accuracy. The metering system adds Spot Metering, which will only take a reading where the “Spot” is on helping you control contrast.
I will eventually come down to what you feel you need in the camera. The increased MP is helpful in cropping out unwanted subjects and still having a high MP count left behind. The faster frame rate helps in sports and action shooting.
Hope this helps.