I don't know how much you know and understand about photography.
From the question you've asked, I presume that you're completely new except probably have been using a compact digital camera to shoot in auto mode just like most casual photo takers are doing.
You may want to start with a prosumer camera (1st hand = $600-$950 or 2nd hand still within 1 year warranty= $400-$700) and still have some money for a tripod ($30-$80), filter, extra memory card, extra battery (or battery charger and rechargeable batteries), flash etc.
Spend 6-months to 1 year reading, shooting and learning, and to find out how strong your interests in photography is.
After that period, you would be in a much better position to decide whether you are willing to spend a lot more money for photography equipment. If you decide to spend more and go into DSLR world or give up photography, then you can still sell off you prosumer camera (probably at a loss of between $100-$400). Possibly too, you may decide a prosumer camera is just what you need and stay put.
Some forumers may strongly advice you to jump straight into DSLR mostly because :
a) they have either gone through the prosumer camera route and now into DSLR, and now think that they should have gotten into DSLR from the start.
However, these people are those whose interests have been sustained and intensified, and therefore are willing to spend much more on photography. So naturally, from their own experience, they would advice strongly going into DSLR straight away instead of going through the prosumer camera route. At the same time but unseen, they are also many who started with a prosumer camera but eventually gave up photography and are no longer here to give advices.
b) they have jumped straight into DSLR for various reasons (e.g. have the budget and/or sheepishly listening to others and/or passionate about photography, following friends, already an old hand in SLR etc.).
Again, they are the ones who have already ascertained their interests in photography by now and so their decisions to get straight into DSLR turn out to be correct. However, they are also many who regretted jumping straight into DSLR but are no longer around photography forum to give advices against jumping in.
Learning photography takes time, money and some hardwork. Your willingness to spend time, money and hardwork depends very much on the strength and sustainability of your interests and how deep your pocket is.
So don't take advices wholesale. Do your homework and think carefully. Different people have different passions, situations and financial positions.