Rehab dilemma - keep it simple, or do it right at the get go

[Alex M.]

I'm sure I will one day regret all the "stupid" and embarrassing questions I am asking online right now - but for now the help is appreciated, so here goes:

I have a small single family property that I just purchased. It's a 140 year old row home. 960 sq.ft. In decent condition - but the last tenants were disgusting. They managed to infest the building with bugs, destroy walls, urinate everywhere, and generally leave the place looking and smelling like a total POS.

When I was buying it, I went through, generated a scope of work that would result in a clean, simple, functional and cute home. I had a LOT of contractors come bid on it, and selected one to do the work for $5000, plus materials. I will still need to do some painting, and minor projects myself after this, but it would get me the repairs and upgrades that I need - electric (outside wiring, 220 for dryer, GFCIs, new 3-ways, etc), window/door capping outside, new hardwood floors installed throughout, demo, new bathroom - floor, joist repair, tiling, vanity, toilet, lights, etc.

The problem is, once I started opening things up, I saw that the "filth" from the previous tenants had infiltrated the ceiling space between the upstairs and downstairs - I'm removing a small section of ceiling to repair a minor leak and fix a couple of joists. On seeing this, my initial reaction is now to want to keep ripping it open. If I were to live in this house, I would not want all this grime and grit in the home - even if it were inside of walls and other cavities. I do understand that this will increase the time and cost of the rehab, but, perhaps naively, I want to do things right the first time. 

Does anyone reading this have experience with older homes? Have you had to decide between covering up surface issues, or fully removing older materials to get the old funk out of a building.

I know it is going to be way cheaper for me to just keep things as it is - new paint and a small bit of patching and the walls and ceilings will look just fine (I plan to rent this between $1000 and $1200 for a 2-bed, 1-bath SFR with a great little yard). However, I plan to hold this for 10+ years, as the neighborhood is trending in a very positive direction, and rents are bounding upwards, as are property values. Does it make more sense to throw down some extra money up front and just "reset" the property to a clean and mostly new state? If I do that, am I risking encountering a world of problems behind the walls? ...If I don't am I risking encountering ongoing problems with a property that has many old features?

Thanks for your help with this dilemma...