@cleanshirt At the most basic level, think of it as a series of boxes, some of which are packaged together, while others stand separate.
CD transport
DAC
Turntable+cartridge
Phono preamp [amplifies signal from cartridge]
Preamp
Power amp
CD transport+DAC=conventional CD player.
Preamp+Power amp=basic Integrated amp.
Now, many Integrated will also include a Phono preamp, but not all. Be sure to check. If you have a free-standing Phono preamp (MM and or MC), you don't need one built into your Integrated. An increasing number of Integrateds also include a DAC, in which case you only need a transport (or another digital device) to do digital. If you're not interested in digital, you don't need this. Some Integrateds with built-in DAC will *also* have built-in Phono preamp, but not that many.
Making a firm choice re. one component usually reduces the options re. the other components, though the record deck/arm/cartridge choice really doesn't. It just tells you whether you need an MM and/or MC Phono preamp (either free-standing or built-in).
Those are pretty nice speaker models, you might look at ELAC and Vandersteen too. Different people will tell you different things about where to start--at the head of the chain (source) or the end (speakers).
As you're firm on the LP deck, my personal recommendation would be next to "audition" some speakers in your price range. No amount of reviews can tell you what your own ears tell you, and once bought, you're living with the results on a day-to-day basis for some time to come.