This is my first year building a rink and I did a ton of research into the "right" way of doing it. If you want to go with commerical options there are basically two big players.
1. Nicerink
http://www.nicerink.com/
This appears to be the most popular option from various pictures I've seen on the web. I didn't go with them for a few reasons. One they are more expensive than option 2, and I think the approach that the second option takes makes more sense.
2. IceNgo
https://www.icengo.com/sections/26/ice_ngo_pro.html
I went with the pro 21'x41' kit, at $299 it was about $40 cheaper than a comparable kit from Nicerink. Structurally I like that their brackets 13" high, that they build the top of the frame with 2x4s and that the liner actuallly sits inside the boards. I think this will lead to a stronger rink and more likely that I can reuse the liner year after year.
The bad news so far is their customer service is basically non existant. I ordered my kit on 12/1. It's now over 2 weeks later and I still don't have all the pieces. It was 5 days after my order that I finally got any kind of confirmation, which came in the form of a tracking number. Delivery from that point took another 5 days. When it finally came I was pretty upset to see all they shipped was the liner; no brackets, spikes, instructions, etc.
I contacted them and they responded that they will contact UPS and get back to me. I knew this was BS as the tracking info I was given only showed a single package with a weight much to light to be everything I ordered. It was clear they screwed up and only shipped a liner. After a few more emails explaining what I knew happened, they finally replied back with just another tracking number. No mention of their mistake. It's currently in Buffalo and honestly I have little faith it's actually the rest of what I ordered. It might be language barrier, as I believe they primarily speak French, but their level of service has been some of the worst I've ever had with an online purchase.
So at this point I have all my lumber cut and rink rake built, I'm just waiting on the rest of the rink kit. The good news is it's been unseasonably warm in Chicago so far so I wouldn't have ice at this point anyways.
Here are some pictures of the planning/area/frame components as well as the rink rake. If you have any questions, feel free to ask!
I have put in a backyard rink for the past 7 years. Each year I try to refine it and find out what works...what doesn't......and so on. If you are going to have your ply on the outside of the liner may I suggest that you paint the sheets white. Trust me on this one. Even a 20 deg sunny day will cause the edges to melt as the wood will collect sun/heat. The white face will help reflect it.