Yes, it's possible to replace your internal SATA drive with an SSD.
Read the iFixit iMac Intel 27'' Teardown guide to make sure you have all the tools/space to do that, it's not hard, but it requires you to be careful and do it with patience, especially when removing the screen (which must be done using suction cups).
You can replace the Optical Drive with a Data Doubler and install any SATA drive in it. For example using the OWC Data Doubler. Plan all this ahead, since you only want to do the iMac disassembly once. ;)
Make sure that the Data Doubler is compatible with your model (if not available you might have to wait a few weeks before they release a compatible model, it has always been like that).
That way you'll have an additional SSD Drive.
Regarding the second part of your question, yes, you can either put the original drive (1TB) in the Optical Drive and put the SSD where the original HDD was or you can install the SSD in the Data Doubler and boot from there.
You can always install OS X in the SSD, boot from it, migrate some information from your 1TB drive and when you're ready, format the old 1TB drive and use it as a secondary drive for whatever evil purposes you want, like to store your Home Folder (search Ask Different for instructions on how to do that).
In the Mid 2011 iMacs (both 21.5" and 27") Apple left enough room for an extra SSD. So if you want to put an SSD inside your iMac you can do that without replacing the DVD drive and/or original hdd. If you're going for an external one you should indeed opt for a SSD with a Thunderbolt connection, otherwise you kinda loose the speed advantage of a SSD.
If you want to separate the OS and application data from your media files, that's entirely possible and there's more than one way to achieve that. Read this and decide for yourself wether it's easy:
SSDs will only get better and cheaper over time so it can make sense to wait, but since they'll keep getting better and cheaper you could also wait for the rest of your life but SSDs are becoming mainstream now so it is safe to make the jump.
Remember that if you install a SSD in your iMac yourself you will loose your warranty so it may be worth to let an Apple Authorized Service Provider do the upgrade for you. If you insist on doing it yourself you might find the following link useful:
Good luck!
Best Answer
The 2009 iMac does not support Internet Recovery, so you'll not be able to download and install Mac OS X directly from the iMac without any external installation medium.
You'll to acquire the installation DVD, insert it into the drive and power on the Mac while holding down the C key on the keyboard.
If you have another Mac, you could possibly download the installation DMG from the App Store and burn it to a DVD or transfer to a USB drive for the iMac.
Another option would be to request the installation discs in an Apple Store - if they still have a supported OS for sale.
A third option is to use eBay or similar to purchase a used installation disc.