As Matt suggested, I would go and get some demos. At the very least this should give you an idea of what you can get for your budget. I would also try to demo something 2-3 times your budget so you can get a sense of whether this is the start of the slippery slope into AV or you know you'll be happy with a relatively budget system. In other words do you get a package system, which on the whole can't easily be upgraded, or you opt for a separates system, or even the basic parts of a separates system, with an eye to gradually upgrading as funds allow.
If you already have a reasonable hi-fi then just running the 2 channel output from the TV or DVD should give you a boost in sound quality. You may need to check whether the DVD player will convert the 5.1 digital sound into a 2 channel analogue output and has the requisite 2 channel output (let us know the make/model and we can advise). Or as suggested, the TV may have an audio out, again make and model would help.
If you decide on a surround system, and plump for the separates route then consider doing it in stages. Some people, including me for a while, and others that have already commented, are happy just using front speakers. Arguably the most important speaker in a surround setup is the centre speaker, since I think on average something like 70% of film audio is dialogue, and you really want that keyed to the display, which is what the centre channel does. So you could opt for just the front three speakers (a 3.0 system). If you find that the extra bass a sub-woofer offers is something you think is important for your viewing pleasure then add a sub-woofer (a 3.1 system). As mentioned, a very good SW can cost thousands (eg the Velodyne DD range) and those that own them can pour scorn on the cheaper models (eg REL) since the quality of the bass is not that good. This is something where I feel if you are coming into AV for the first time, and you can't tell the difference between 'good' and 'bad' bass, a relatively cheap sub-woofer will enhance your viewing pleasure (as long as it is sited carefully). People with expensive systems have often got to that point over time through various upgrades and have come to appreciate the differences a better quality system can offer.
In other words what I'm saying is don't be put off by comments you may get about buying a cheaper system, we all have to start somewhere, but try to demo anything before you buy to ensure that you are happy with it.
Lastly you can add rear speakers, which ideally should be the same as the front speakers, at least in the same model range, but they are only really effects speakers and something smaller and more discrete would be sufficient initially.
Another area that I consider important is speaker placement, even with budget systems. More often than not speaker size and placement is a compromise between aesthetics and real world room use and the ideal world. However do try to consider your room layout, if speakers can not be positioned in the generally recommended places (this is often the case with rear speakers) then consider whether you do without them. You may end up with a system that either spoils the surround sound field or the speakers are too far away to get the proper effect. You may be better off spending more on the rest of the system.
You may also want to ensure that the system is future proof for HD material. This would mean ensuring that the surround amplifier either has an HDMI input and can decode the new HD surround formats, or has a multi-channel input that can receive the decoded audio from the Blu-ray player (which itself must have a multi-channel output).
Gosh, just realised how long this post is, my apologies if any of this is simply muddying the water, I hope it is of some help. As pointed out, coming into AV for the first time can be daunting, but like TrimTheKing, I would be more than happy to offer advice here or offline.
