If by the Hornady you mean their LnL AP progressive, do not start with that. I have one, it's great, I'd recommend it to you later--but I believe those just starting out should start on a single-stage press.
A turret really isn't any faster than a single-stage if you're doing volume production. All it will do is save you time switching dies, which a single-stage Hornady LnL press will allow you to do easily w/ the LnL bushings.
But get a single-stage to start. You can learn the individual steps of reloading that way, you'll want a single-stage later on anyway even if you get a progressive.
The name of the game is to think about where you want to be in 3 or 6 months--and the best thing to do is learn well and deliberately. It's not a race, and spending just a little extra time now, learning the steps, mastering them, means you will be that much better grounded later.
Having learned on a single-stage means that you can turn your attention to the specifics of progressive reloading when you get there, without having to determine if issues are related to the press, or the process.
A great compromise between the Hornady LnL Single-stage and being less expensive is to get the Lee Classic Cast single-stage press. It has an insert that can be removed and replaced with the Hornady insert, which then allows you to use the LnL bushings for easy switching of dies.
Hornady Lock-N-Load Press and Die Conversion Bushing Kit
which goes in here:
Lee Classic Cast Single Stage Press
The two of those, together, are about $100 (and the press goes on sale from time to time). They're equivalent to the Hornady offering, which costs $131.99:
Hornady Lock-N-Load Classic Single Stage Press
I have the Hornady Progressive press, and I love it--but I also bought the Lee Classic Cast press (with conversion) to go with it, replacing my older RCBS Jr single-stage press: