Roll both previous employer accounts into the Vanguard account
You can do this. Or you can roll over either account individually to your new 403b. Whether you can roll over existing pre-tax accounts into your new 403b will depend on the specific rules of your new plan, but most plans allow for it.
roll the two previous employer accounts into the ROTH
It sounds like your previous 401k and 403b were both pre-tax, and not Roth accounts. If this is the case you would pay tax at your marginal rate on the amount rolled over to your Roth.
Is there some other option I'm missing?
There are 2 other options.
1) Roll them over to a traditional IRA. If you do this there will be no taxes due and they will stay as pre-tax accounts.
2) Do nothing. If the fees and fund options for those previous accounts are as low as they are for your new 403b or traditional IRA, there is no need to do anything.