I'm too long out of touch with it to want to make any informed suggestions, but (at the possible risk of stating the obvious)
turn2us have a benefits calculator
here
local council's website should say somewhere what the council tax rates are there.
local housing allowance rates
here, (it's not always as simple as all of one council's area being the same LHA rate - Lewisham for example is partly classed as inner London, part as outer London) and how many bedrooms you're entitled to for LHA
here. (not sure if it's possible to get entitlement to an extra bedroom if someone in the household is disabled and needs more space or anything like that.)
i think that now, you generally claim a housing element of universal credit, rather than claiming job seekers' from the job centre and housing benefit from the council (although there are some exceptions, and i'm not sure how council tax benefit works now.)
one complication might be
renting 2 bed, joint tenacy privately
i'll put this in a way that doesn't ask questions, but there is always a chance that with means tested benefits, they will try and say you're a 'couple' if you're merely sharing a place with someone else, even if you have separate bedrooms.
a 'partner' in benefits speak can be same or opposite sex, married / civil partnered or not (it's one of the few bits of 'the system' that recognises common law couples)
simply sharing a house / flat with someone doesn't make you a couple, but you may have to argue about it, and state (maybe even show) that you have separate arrangements for buying / storing / cooking food and doing laundry and things like that.