What uniform adjustments should I be concerned about when wearing the uniform years after getting out? What headgear is appropriate?

If you bought a new uniform, I assume it's the blue ASU, follow Army Regulations for wearing that uniform. I recommend a "wheel hat" for a funeral because it's a formal military ceremony. Otherwise the black beret, unless you're allowed to wear one of the many special colored berets. Back in the 70s I had the honor of doing several military funerals as an Honor Guard OIC. We all wore Service Dress with Wheel Hats except the firing team who wore blue berets (wheel hat was clumsy to wear and fire a weapon).

First, let me offer my condolences on your family's loss.
Next, I can only speak for USAF instructions on wear of uniforms and GENERALLY speaking, an AF Retiree has two choices: 1 The uniform authorized for wear at the time of his/her retirement or 2. the currently authorized uniform. (Yeah, I know, the AF changes uniforms like most of us change our socks) The AFI also states we should meet weight and grooming standards and we are required to wear the AF Retiree pin on our lapel to indicate we are retired.
That said, as MiL requested you honor FiL's service, If I were you, I would wear the uniform I was authorized on my last day on AD.

Honor Your Father In Law with what you feel in your heart, if you were authorized to wear a Stetson at Discharge wear it, as for DUIs since you are no longer with a unit you should not wear them, wear your uniform with Pride YOU Earned It, Sorry For Your Loss But Know He is in a Better Place