My personal opinion (noting I have owned large f number refractors and once when I was a teenager a 4.25" reflector so my baseline is biased) is any one of the three would be fine.
I can only speak from looking through my 70x900 and I enjoy the views, especially coupled with the GSO 15mm (60x and >1 degree FOV is nice). The 25mm that comes with the telescope is fine to start viewing clusters, M42, 47 Tuc, Omega Cent, the wonderful open clusters near eta-Carina, the Jewel Box etc. The eyepieces that come with the telescope easily split Acrux and Alpha Cent etc. and I see down to around 11.8 magnitude from my suburban skies. Jupiter is small but you can easily see the bands and if the conditions are good the shadows of the Galilean moons as they cross the disk if you beef the magnification (go to 90x or so). The phases of Venus and Mercury are readily discernable. The Moon is a treat at any magnification.
I think the 500 or 700mm will be equally as okay as the 900mm, might get a little more colour distortion (usually blue edges) as you get shorter focal length, especially noticable on the Moon and Venus, Jupiter etc. and you will not get as much magnification as with the 900mm as noted before.
Whilst Andromeda galaxy is up (low though) good views can be had, NGC 253 is also interesting to view (plus other galaxies) although to first time viewers they can be a little disappointing until one learns to appreciate what they are and how to adapt the eye etc.
As other have said get a strong mount, say the AZ3. The logic of the AZ is straight forward the EQ takes some getting used too.
Yes DSO is deep sky object, generally associated with galaxies, nebulae and other faint fuzzies.
Final question that might help with the 500mm, 700mm & 900mm question (for example and assuming magnification is not the driver) is how dark is your night sky? If you are in suburbia then go longer as it will give darker backgrounds. If you live where there are dark skies that make everyone else drool then any focal length works.
If you choose a reflector then hopefully someone else can help as it has been too long ago for me
