Can't help on the projector, but laptops are not particularly resilient to knocks due to how fragile the screens are. There are however specific laptops called 'toughbooks' available which are commonly used by contractors and service engineers etc. Panasonic do a range of toughbooks in various levels of 'toughness'. (The name toughbook might actually be limited to panasonic, but I am sure other manufacturers will make similar kit) The downside for this resilience is price. The alternative is to buy a standard laptop and a durable bag/case for it.
With regards speed, nearly all new computers come with Vista now, so you should be looking for at least 2GB of RAM, and a core 2 duo processor. A duo over 2.0Ghz speed will run very well. If you can get hold of an XP system then it will run well on a considerably slower system.
When you say average to below average, what actual range are you looking at? Around £500 will get you a good one for your purposes. There is an acer, 4gb of RAM, 2.0GHz Duo, with blueray player for about £500. (The blueray will play DVDs)
Is there any reason why you intend to replace it regularly? Providing you don't 'clog it up' with all sorts of crap software it shouldn't slow down too much over the course of a few years. People tend to update their computers too often, when a simple reinstall will often make most computers nice and quick again.