Like with many things, with armor one must start from the outset by asking the question: "What do I want this for?" The answer will inform your very first steps and all the following ones. And keep in mind, you can always change directions later and do something else. You may not be able to use much of a D&D LARP outfit when switching to mid-14th century knight, but there's no reason you can't have two outfits for two different functions. I mean check out Sir Wolf, he's got like 30 different kits.
If you do decide to go historical though, there's more to it than just going to living history events. The incredible journey of learning it has taken me on to get all the details as right as I can was something I never expected. Because to be truly historical, you have to know a lot of things that aren't obvious. Start with a harness and pick any single piece of it. To be historical or rather to even know if you're being historical or not, you really need to know everything from what material it was made from and why that material and not another one that the same craftsperson had at their disposal, to things like what impact his religion had on how that guy made that item? Looking deeper into everything from points to swords will reveal to you one bit at a time an entire world, and with each new piece of the puzzle the entire picture and feeling of medieval life will come into greater focus in your minds eye. All that from undertaking to build a historical armor!
Maybe that all makes me sound like a royal nerd, but it really has been an amazing journey of discovery.
Scott