I just finished measuring my backyard and was going to order my liner and buy some boards at Home Depot. This is my first year building a rink and wanted to get an opinion on what size liner to buy, how high the boards need to be and if there is a preference between NiceRink or IronSleek. I can either build a 52'x42' rink with a 20" slope or a 45'x42' rink with a 16" slope. Since it is my first year I am thinking that the smaller rink is going to be easier to build and then maybe move to the bigger rink next year if everything works out.

For the 45'x42' rink I am thinking about buying a 50'x47' wide liner from NiceRink and then use 16" boards on the shallow end and 24" boards on the deeper end. Should I use the same board height around the entire rink and should I get a bigger liner for the higher boards on the deeper end?

16" of slope is quite a bit, and it will mean you have 20" of water in your deep end. It's not a dealbreaker, but it makes it quite a bit more difficult and will require a LOT more bracing than if you had a more manageable slope.

I tend to build wooden rinks with the same height boards all the way around, but you can certainly go lower in your shallow areas (provided you are 100% confident in your slope measurements).

As for the liner size, I always get more than I need. Your numbers above WILL work, but it doesn't give you much wiggle room. Those sizes you mention are the bare minimum size liner you can use for those size rinks.