I just ordered one of these kits. They include:

Lee Classic Turret Press
Lee PaceSetter Dies (3 Die set)
Lee Auto Drum Powder Measure
Lee Saftety Prime System (Large AND Small)
Lee Auto Disk Riser
Powder-Thru Rifle Charging Die
Case Lube    

I have also ordered spare turrets and die sets, a digital scale, tumbler, bullet puller and digital calipers.

I am completely new to this and just want to make sure that this is everything needed to comfortably start reloading. (Aside from brass, bullets, primers and powder of course)

I am excited to finally get into reloading this year. I had a kit ordered the day before sandy hook and everything went to shit so I cancelled it.

Anyway, if anyone can confirm that I will be able to start with this setup I would appreciate it. Thanks.

If you're loading for a rifle you will want the appropriate trimmer and chamfer/debur tools.

What calibers will you be loading for?
Type of rifle.....semi auto, bolt/lever action etc.

AR type 5.56, 9mm semi auto handgun, 44 levergun. Maybe 45acp and 300blk in the future. Any recommendations on budget trimmer and chamfer tools?

You will definitely want to be trimming the .223/5.56 brass.
I wouldn't worry about trimming the 9mm and .45 brass.
I can't speak to trimming the .44 brass as I am not familiar with loading it.
The cheapest option is the Lee trimmer lock stud/guide/cutter combo....but it is tedious and will quickly become your least favorite part of reloading.

I personally use the CTS trimmers for .223 and .308. But they are about $42 each and are caliber specific. Worlds above the lee stuff though.
(google cts trimmer)
Depending on the volume of brass I need to trim I either use my hand drill or chuck the trimmer into my drill press.

For chamfer and debur I use the Lyman Case Prep Multi Tool. It's like $18 on amazon.
Again, depending on volume of brass I will most often chuck the tool head into my hand drill or drill press. I really quick light touch and it is ready. If you're not careful you can ruin the brass.

When I process .223 it is usually 1,000 or more pieces at a time.
I recently trimmed/chamfer/debured 3k pieces. It kind of sucked. Wear good gloves.

There are many other options for trimming/deburr/chamfer so hopefully others will chime in with other options.

Thanks for the recommendations.

You should have a rifle case gauge at the least, better option would be the Hornady headspace comparator tool.

This takes all the guess work out of shoulder setback.

A couple different reloading manuals, along with everything else mentioned above.