I started bowl turning before I started pen turning. IMO the absolute must haves are: a 4 jaw scroll chuck, a 3/8" bowl gouge, and a face plate. As always there will be some conjecture on these recomendations but from my experience, these are the 3 tools that made my learning curve the easiest. I have expanded my arsenal to include a 1/2" bowl gouge and a 1.25" Crown bowl scraper.
If you haven't, pick up Keith Rowley's "Woodturning - a Foundation Course". It is good reading material as an intro into turning in general, and has a section dedicated to turning bowls and the like. After you are done, Youtube as many bowl turning videos as you can - this will help you observe tool presentation and such. Also google Richard Raffan and his techniques - here is a sample:
http://images.taunton.com/roughturning.pdf
FWIW - the method that I found easiest was to mount your blank to your faceplate, turn the outside of the bowl and leave either a tennon or a recess (depending upon the diameter of your bowl) Be sure to sand, decorate, and finish the bottom of the tennon/recess as you won't be able to do that again while on the lathe. My method for turning the outside of the bowl is to start in the middle and pull the gouge through to the shape I'm looking for. After turning the outside shape of the bowl, mount the tennon into the scroll chuck and begin hollowing - to hollow, either create a dimple in the middle and work towards that dimple, or drill a small hole and work towards the hole from the outside in - don't drill too deep.
Finally, with regard to wood selection - turning green is generally easier when first starting out because the wood is more forgiving - i.e. you can take larger shavings, it is easier on your tools, etc. - however, you will find that turning green wood will require that you either rough turn, bag, wait - or turn very thin (1/4") walls and let the piece warp. Also, you will notice more pronounced tear out with green wood as you encounter the end grain - with good tool presentation and use of a shear cut, you can overcome this - but don't expect to eliminate it at this stage without a lot of sanding. Further, before you apply your finish, you will want to wait until the moisture content in the bowl has equalized.
With all that said - I don't recommend you start with green wood - you will likely become down on yourself for not being able to produce a bowl free from tearout and/or checking due to moisture loss. I recommend that your first 2-3 bowls be turned from a dry, mundane piece of maple or cherry - with mundane being code for stable and no more than 3" thick. You should be able to find something relatively cheap from your local hardwood dealer (or someone here on the forum). Once you have the hang of it however, start turning that wet wood. You will quickly find that most of it can be had for free, it is easier to turn, and can yeild you good results once you have your techniques down.
With regards to shape and size - I recommend turning cereal bowl size/shape first - they are easy to deal with and shouldn't cause your lathe to dance around too bad. Use good screws in your faceplate, you don't want your bowl flying around the shop. Don't stand in the line of fire - i.e. off to one side (in my case, I'm always behind the bowl) Wear eye protection. Same rules that apply for pen turning - good ventilation and a dust mask are required.
Feel free to PM if you have additional questions...
