I'm moving my electrical meter due to our new kitchen addition. The new meter will feed two 200 amp panels. The first panel will be approximately 130' away and the second will be 230' away. What type of wire should I use for these runs?

Whatever wire your electrician uses will be fine. I am sure he knows what he is doing.

You did contact the power company to get their approval to move their meter.

Opps, sorry, I'm sure your electrician will do that for you.

I would use THHN/THWN in PVC conduit. I would use stranded, don't know if they make solid in that size.