Yes, if your budget is $600 and you're starting out, the D40 is a superb choice. There are definitely some limitations with the D40, but you can live well within those limitations and still get professional quality images, if your skills are up to it.
Other people have mentioned options like film cameras or used digital SLRs. I cannot recommend a film camera if you're starting out, simply because the cost over time for processing film is too expensive and there's no instant feedback (i.e. no LCD) which slows learning techniques and skills. A good quality film SLR (used) would be $200 and film/processing/printing @ $10 per roll means in as few as 40 rolls of film (or 960 images) you'd be over $600.
As for used, I can't recommend that you get a used camera with no warranty. Moreover, the D70 someone mentioned has a very noisy sensor above ISO 400, which is why I upgraded to another SLR. If you're going to buy used, I'd get a D2H, which is a pro-level body that sells for around $400 used (although it has other issues like 4.1 megapixels and issues with the metering system).
Really, the only differences between the D40 and more expensive cameras would be a few items. Let's examine those in greater detail.
1) the autofocusing system
--the D40 has a much simpler autofocusing system than more expensive cameras. However, the D40's system works great. The more complex systems are designed for specialized purposes. In general usage, the differences are negligible. Unless you do a lot of specialized shooting (all sports, all low-light, etc.), you won't see the difference in day to day shooting.
2) the metering system
--the more expensive cameras have more evaluative segments or areas. It theoretically allows them to make better exposure decisions. Ironically, since you're starting out, the simpler system of the D40 works in your favor, allowing you to look at a scene with your eyes and learning how to evaluate light when working with your camera. I consider the difference here not important for your purposes; you're better served learning how to evaluate a scene with your eyes and the D40 will work just fine in metering, especially as you gain experience.
3) The lens compatibility issue
--The D40 requires you to use AF-S (or Sigma's HSM) lenses, or lenses with built-in focus motors. At first glance, this would seem to be a serious limitation, until you look at which lenses do have built-in motors. There are some fine lenses that you can use, like the 24-70mm f/2.8, the 70-200 f/2.8, etc. All are expensive and outside your budget at the moment. Generally, the stock lens is the 18-55mm AF-S VR lens. That's a great starter lens and is generally better regarded than Canon's equivalent (which is still a good lens, Canon-fans). As your skills improve, you can still add AF-S lenses and Nikon is adding more AF-S lenses all the time. And the regular AF lenses will still mount and meter (they just won't autofocus). So you can still use great lenses like the Nikon 85mm f/1.8 and get good exposures.
Note that the D40 does all the things the big boys do: control aperture, shutter speed, ISO, shoot RAW, iTTL flash system, etc. In other words, where it counts, the D40 can deliver.
Generally, what I would suggest is that you get the D40, the standard 18-55mm VR and for any upgrades, work on lenses, lighting, education, and practice.
Lens upgrades:
55-200mm VR AF-S
70-300mm VR AF-S
either of which will get you more telephoto and which should AF with the D40.
Lighting:
SB-800 or SB-600 flash
Education:
Take some photo classes or at least read some books and practice the techniques therein (controlling depth of field, creative use of shutter speeds to stop/blur, composition, creative lighting, etc.)
Practice:
Practice, practice, practice.
Hope this gives you confidence that you've made the right choice. Don't let the other answers confuse you. The D40 is a great camera to start out with and as you grow, the camera will still grow with you and still get great images.