The type of repairs also varies based on the loan type, here's some information pasted from (not my site) https://themortgagereports.com/18228/which-fha-203k-loan-home-construction-standard-streamlineThis is the work which is allowed via the FHA 203k Limited: Repair/replacement of roofs, gutters and downspoutsRepair/replacement/upgrade of existing HVAC systemsRepair/replacement/upgrade of plumbing and electrical systemsRepair/replacement of existing flooringMinor remodeling which does not involve structural repairsExterior and interior paintingWeatherization of windows and doors, insulation, weather stripping.Purchase and installation of appliancesImprovements for accessibility for persons with disabilitiesLead-based paint stabilization or abatement of lead-based paint hazardsRepair, replacement or the addition of exterior decks, patios, and porchesBasement remodeling which does not involve structural repairsBasement waterproofingWindow and door replacement and exterior siding replacementWell or septic system repair or replacementAnd, this is the work allowed via the FHA 203k Standard: Major rehabilitation, such as the relocation of a load-bearing wallNew construction, including room additionsRepair of structural damageRepairs requiring detailed drawings or architectural exhibitsLandscaping or similar “site amenity” improvementAny repair requiring a work schedule longer than three (3) months; or rehabilitation activities that require more than two (2) payments per specialized contractorImprovements that require a plan reviewerImprovements that result in work not starting within 30 days after loan closing; or cause the owner to be displaced from the property for more than 30 days during the time the rehabilitation work is being conducted

You may be required to have the septic and well inspected and there may be requirements to upgrade the systems to current code if you are pulling permits to do extensive work on the residence. 

If you're confident in your numbers, I would use the cash to upgrade the property, then get a HELOC.

Only you can decide the relationship part of this, but look at it from a renter's point of view (because that is what you would legally be)... if you were renting from me, would you agree to help pay for my upgrades/rehab to the house?  

I have read a lot of articles on what to upgrade, remodel repair ect.

If I were you I would do further research with environment organizations that could give you more information on how to test for it, how to remediate it and how to make that decision.I will say that if you are planing on adding/upgrading the Air Condition I would suggest you work with an asbestos abatement company to do the work for that portion of the house.

If you use an LVL to carry the ceiling load then you won't have to upgrade the rafters for structural reasons but you will have to pad them down to get the insulation in unless you spray foam it which is very expensive.

Any good references to a reliable, cost-conscious handyman in this area?

It took us a few months and a fair amount of money to upgrade all of the units and the exterior & turn over the tenants for higher paying ones, but we lived in one unit and rented the other 3 units for 4 years, living rent free in our unit and cash flowing $500-$700 a month on the other 3 units. 

There are certain other things that we always repair on our flips such as water heater replacement if they are near end of life, appliance upgrade, etc.