After using my keezer for a few years, I can't recommend foam insulation on the inside. As the keg goes in (40+ pounds), it may scrape the sides. I dunno - maybe y'all are stronger than I am. Wood can take a lot more abuse. The thermal loss of 2x wood versus another inch of styrofoam isn't much.
As an added bonus, I created some auxiliary refrigerator space for my (wonderful) wife by installing some opened eye screws to hold the freezer baskets. Made the project a much easier sell.
I used 2x6 wood on top of freezer with truck bed insulation taped on bottom and then wrapped it with stained 1x8 pine on front and side walls. Then used about 3 layers of reflectix insulation bubble foil on the inside on the wood collar.
First time posting photos on here, so please excuse me if they don't attach correctly.
I just finished my keezer build a couple months ago. I went with 1.5" cherry, 1.5" foam backing, and then wrapped the inside with aluminum sheet metal. I'm really glad I went with the sheet metal. Not only does it look super clean, but it protects the foam from getting beat up lifting kegs in and out.
I spent about $100 on the cherry wood and had enough left over to build a skirt for the bottom which helps to conceal the casters.
I use PVC lumber from Home Depot, more expensive than would for sure, but perfectly flat and you can either use the fake rain outside or turn it inside for a smooth surface which is my preference. I wish I would have painted it black in retrospect, as it is a little bit more prone to staining then wood with a slippery finish would be. The PVC offers great insulation qualities I think comma evidence by it always feeling room temperature when you touch the outside. It was very easy to drill into and I got extremely tight mitered corners.
As for Wood...I am a Wood Lover...So I select the wood I want to see...Walnut, Mahogany, Northern Red Oak, Alder, Maple,or maybe Cherry...not a cheap wood stained to look like something else...Even Pine is beautiful with a clear finish on it.....But I owuldn't stain it cherry or oak...
Every Wood worker has their way of doing joints...Myself I would consider dovetails If the ends would be exposed.