I have no experience with projectors, and am just starting to look for a home projector for viewing family snaps and videos etc. A few questions, does the resolution of the projector (800x600 or 1024x768) have to match the laptop resolution, or can it be independent?
Will most projectors also plug into dvd players for projecting movies and TV?
Recommended brands for price and quality?

I recommend visiting projectorcentral.com. They have all the info you'd want to know, and more.

As to your qs: resolution can be different than your monitor, but having it same makes things slightly easier, as what you see on your monitor is the same as on the screen. Most (I'm sure all modern) projectors plug into a DVD player. But projecting for movie use is a totally different beast than making presentations and slideshows. If you want to watch movies, you'll probably need a widescreen 480p (at least) projector, whereas for presentations/slideshows you'll probably want a 4:3 aspect ratio projector with a powerful bulb.

For family use save yourself a lot of bother and expense and just get the largest HD TV you can afford/accommodate. To guard against obsolescence make sure that it has:
1080p
hdmi
PC input.

You will then have the choice of either using a minimal spec PC for your input (or any laptop) or if you have kids get them a Playstation 3. The latter has a great slideshow mode, plays Blu-Ray discs, Luminous Landscape downloads, etc. Actually IMHO worth the price even if you do not put a single game into it. Perhaps also the XBox. Probably the best TVs at the moment are the Sony offerings, LCD panels or the rear projectors. I have a 70" rear projection TV and with a Playstation 3 makes a great way of storing and viewing family pics. The 60 giga byte hard disc can store thousands of 1900 pixel-wide jpegs. That's the largest size you need for HD TVs. Some HD TVs even have card slots. If you insist on a projector have a look at the latest Sony offerings, but again make sure those 3 items above are present.