Newspapers can use non-joyo kanji, though it is customary to include furigana when that happens (or even when using joyo kanji in words that are read in an unconventional way).
It's important to note that what newspapers consider joyo doesn't fully line up with MEXT (the Japanese Ministry of Education). The main goal is to make it easier to read for the general population, so obscure joyo kanji might appear with furigana, but common non-joyo kanji without.
Michael has a set of lists called 常用漢字 / Joyo Kanji (divided by grade) that I highly recommend. If that order doesn’t appeal to you, mysticfive has 21 lists that present the 常用漢字 in the official order.