I'm a little confused on the different types of panels out there. What is the difference between "Main Breaker" and "Main Lug" panels? Which should I get to replace my sub panel?

In 2011 I had a new Main Panel added and my old panel became a sub panel. My entire 1500 sq ft house was on just 8 breakers at the time. The new main panel is 125A the old panel is 70A. The two panels are connected by a 600v conduit.

I have moved most of my circuits to the new panel as I remodeled my house (yeah for grounded outlets!) The sub panel will be used for my kitchen remodel since it is right outside the kitchen. I may need more than 8 breakers if I do dedicated breakers for each appliance, so I want to replace the sub panel with a 10 to 12 breaker one. I'm also concerned that the old breakers aren't grounded, so I don't want to use them with new wire.

What should I be getting? Is there a limit to the amp size base on the conduit load? I'll post pictures of what I have in case that helps.

 

Main lug is simply breaker panel without main breaker. You don't need main breaker in sub panel if it is within same building.
Your current sub panel is main lug.

You can simply get a main lug load center with 12 breaker space and move everything over. Your existing panel is grounded. Bus bar at the bottom is ground bus bar. (where bare copper wires are attached.)
When you install new panel, do not bond neutral and ground. Usually there is a ground bolt through neutral bus bar and many panels don't come bonded (either have bolt backed out or not installed)

You will also have to purchase ground bus bar as most panels don't come with one. It will be attached inside breaker panel on to the metal box it self.

I see that you also have a thick aluminum cable. You have have to apply anti-oxidant compound/grease to the wire before installing.
What is that wire for?

Your feeder cable to sub panel is 4/3 NB-B, so maximum load you can have in the sub panel is 70A.

 

Your panels are connected by a cable with insulation rated for up to 600 volts.

A main breaker panel is one with a breaker to turn off the entire panel. You can use one, but it is not needed if it is in the same building as your service panel. The panel needs to be rated the same or higher than the breaker feeding it.

Anti-oxidant is a good practice, but is not required by code.

Breakers are not grounded. Wiring methods and devices are grounded.