Hiragana / Romaji
Words are spelt the same whether using romaji or hiragana, it's the symbols that change. You'll be able to write any words you learn in Hiragana, because it's a phonetic alphabet.
For example in arigatou, the symbols for a, ri, ga, to, and u are used (I can't write the symbols, I don't have Japanese input on this computer). However, learning Japanese also means learning to READ Japanese, and romaji is very rarely used. If you want to learn to read/write Japanese, learn Hiragana early on and practice regularly. If you always read Hiragana instead of romaji, it is my opinion you'll get better faster.