So first what material were you looking at because that radically changes the answer. For instance in the case of chain you'd want to get a whole shirt, where as with plate you might need a gorget (neck armor) to attach the pauldron (shoulder/upper arm armor) to at the top of the shoulder, and leather you might be able to get away with some elaborate strapping configurations. It all depends on what your goals are and what kind of kit you want to put together long term. Armor is one of those things that tends to hang around for a while and it is generally better in my experience to get the higher quality items rather than grab the first cheapest thing you come across early on.
For some context I wear as close to full plate (steel) as I can get within the rules of Dagorhir so this does color my advice, however I've used chain and I have unit mates that have used leather now or in the past.