Retirement tax questions

@Critter#2 Thank you.  OK.  I've reviewed this. Just to be clear. My employer pays for my housing directly and this is reported on my income statement.  Therefore, I need to add the amount my employer pays for my housing to my gross salary + rental income + interest + dividends to get my MAGI.  If this (I am single) is higher than $135K, I am ineligible to contribute to a ROTH, but eligible to contribute to a traditional IRA (given that my salary + housing is more than R$140,500, because rental income and dividends cannot be considered income for ROTH purposes.)  Is my reasoning correct?