I spent months agonizing over my first lathe. I finally went with an 11" Sieg model I got from DroPros. Not only did the lathe fail to perform well, and was way out of manufactures specs, DroPros screwed me over badly.
My advice to start with is: avoid Sieg (they make most of the 7x lathes), and avoid DroPros (they are wonderful until you have a problem then will boldly lie right to your face).
I still have the lathe, it is sitting in my garage on a palate taking up valuable space. You can have it for $1200.00 if you come through central Ohio to get it. The head stock is slightly out of alignment with the bed, probably an easy repair (probably). I paid $2k for it, will toss in the AXA tool post also. DroPros stopped carrying the model when I found the problems, they agreed that if I gave it to Matt at QMT, and he agreed it was out of factory spec, that they would give me full price off any lathe I purchased from Matt. They reneged on the deal as I was loading the lathe to take it to Matt, after I had already paid for my PM1340GT. They just flat out lied about making the deal - and they had the gal to do it in an email thread that actually included the deal.
I suggest you make a list of things it absolutely must have, a list of things it absolutely must not have, and a list of things you would like it to have.
For me,
It must have:
power carriage feed.
power cross feed (you do want this).
Threading dial (this means an Imperial lead screw on almost all lathes. Don't believe the lie, not having a half nut is the suck).
A repeatable spindle mount (This is probably something you also want given what you want to do).
A partial gear box (changing gears to change feed speeds is dumb).
Reversible spindle
Left hand threading (you prolly don't need this).
cross slide travel that is larger than 1/2 the swing (you would be amazed how many lathes don't)
It must not have:
screw on chuck (Screw on chucks are a deal breaker imo, this will include all the old and beloved SB's)
No way to attach a threading dial (they can be retrofitted on metric lathes)
I would like it to have:
variable speed
2" bore (that's pretty big for a small lathe).
coolant (still don't have this...)
All that said, one thing you do not want to be doing is running a piece of 5" stock on a 7" lathe. you prolly don't want to do this on a 9" lathe for that matter.
You should pay some extra attention to compound travel. You are intending to cut tapers on large stock, it is important that the compound has enough travel to cut those tapers.
I doubt you will find a lathe smaller than 10" that will spin a 5" part and cut a taper on it. it is not a deal breaker provided you can retrofit a taper attachment, once again, the lathe must be beefy enough to accommodate a solid taper attachment (prolly 10" minimum again).
Keep in mind that you will want the lathe to do other things at some point. As already advised, get the next size up from the biggest lathe you can afford (just find a way to afford it).
Many of us here own Precision Mathews machines, I have a lathe and a mill from PM. We buy his machines because he stands behind his products extremely well, and he works with the manufacturer to include things that a machine should have. He is experienced with machining, so he understands what a machinist wants. Call Matt and ask him what he suggests, he has a large inventory not on the website.
http://www.machinetoolonline.com/NewlatheIndex.html