Sorting it at closing is much easier than reconstructing it later, and the buckets are these.
Adding to basis means the cost becomes part of what you're treated as having paid for the property, and it gets recovered through depreciation over years instead of deducted now. Title and settlement fees and recording items typically land here. Basis then has to be split between land and building, because land isn't depreciated. People commonly use the county assessor's ratio of land to improvement value for that split, and whether that's acceptable for your return is a question for your tax preparer.
Loan costs like your $2,400 origination are usually treated separately from the property itself and recovered over the life of the loan rather than the life of the building. So they sit in their own asset account, not lumped into the building.
Prepaid interest is interest. The $1,100 escrow deposit is still your money sitting at the servicer, so it's an asset on your balance sheet, and it should get reconciled against the escrow statements you receive. The $780 tax proration credit reduces what you paid at closing and relates to taxes the seller owed, which is why it doesn't behave like income.
The division of labor most people land on is that the bookkeeper records each line to a sensible account at closing, and the tax preparer decides the classifications that affect the return. Whichever way it goes, ask for the depreciation schedule after the return is filed and make your fixed asset list agree with it. That single habit prevents most of the mess I see described in this room.