having the TESOL class experience will definitely be a benefit to you personally, even if the companies don't value it as such... which is really sad, as the companies in Japan tend to have mediocre training). You (and your students) will definitely benefit from what you learned studying TESOL.
don't worry so much about apartments. if you're okay with sharing a house with other people, then there are heaps of guest house options and shared accommodation.
(look at
http://www.tokyocityapartments.com/guesthouses-info/ and
http://roomshare.jp/ and
http://www.oakhouse.jp/eng/index.html. But Berlitz will be a guarantor for an apartment, which means you can go through a regular Japanese agency. like,
http://www.chintai.net/.
Lots of the apartments that the english schools provide are pretty rundown. But, outside of Tokyo at least they tend to be good value. Bigger than what you'd expect to pay for the price. (I was living in a 2DK for 54,000, only 45 minutes from downtown Tokyo and I had friends who were a bit further out with 3DKs for the same price)
but, honestly, i think it's better to be able to choose where you want to live, then be stuck where a company places you.