The renovation money is raised up front and sits in the deal as a separate line called capex, short for capital expenditures. So a 60 unit purchase at, say, 6 million might be funded with a 4 million loan and 2.4 million of equity, where 400,000 of that equity is set aside purely for the unit renovations and roof and parking lot work. It isn't paid out of rent. Rent pays operating costs and debt service, and it's usually too thin in the first year of a value-add plan to fund construction on top of that.
Value-add in strict usage means an asset that's occupied and producing income today, where the sponsor believes rents are below what the same unit would fetch after a defined scope of work. It sits between core, meaning stabilized and already renovated, and opportunistic, meaning heavy repositioning or development. Loose market usage stretches value-add to cover anything with a story attached, including deals where the only real plan is hoping rents rise on their own. When you read a package, look for the scope per unit and the rent comp that supports the premium.
Your read on classic is correct. It's the standard industry label for the original unrenovated finish level, and packages use it to distinguish those units from the renovated ones so a buyer can see how much runway is left.
One thing worth understanding before you look at more of these: renovations only work if you can turn units to do them. If the property is 96 percent occupied on long leases, the sponsor can only touch units as tenants move out, which might be 30 percent of the building a year. That pace, rather than the construction cost, usually sets how long the plan takes.