I have only just now discovered this thread, so--with apologies in advance for a bump some may find disruptive--I'm going to add my two cents' worth, from both sides of the preparedness question.
When I had a 1986 Nissan Maxima, I carried a lot of emergency repair equipment in the trunk, and after twelve years realized that I had used almost none of it except for the jumper cables, the air compressor, and oil change tools (I did oil changes on the road since with the Maxima I could do them with all four wheels on the ground; both of the cars I have had since require ramps). Meanwhile, for the actual urgent needs for rescue and repair I had on the road, the only thing that actually helped was a credit card to use as a pipeline to funds back home. Once I had a slide-off in a snowstorm and the $30 tow fee went (I think) on a credit card. Another time the rear brake pads wore down past required replacement thickness (with > 90% hearing loss in both ears, I cannot hear pad wear indicators), so the calipers started biting into the discs and the brakes felt funny (but still worked, since the front brakes pick up the vast majority of the stopping load) for about 1,500 miles before I could have them looked at. Again, the ~$400 for new brake discs went onto a credit card.
So, with a 1994 Saturn SL2 (former roadtrip vehicle, now just a daily driver) and 2005 Toyota Camry V6 (current roadtrip vehicle), I carry just the bare minimum--jumper cables, air compressor, and tire pressure gauge--plus equipment and supplies tailored to the specific needs of the vehicle. For example, the Saturn burns oil at a rate of 1500 MPQ (poor drainback and oil temperature management lead to ring coking, so the rings stick and don't wipe the cylinder walls adequately), so I have to carry oil if I am road-tripping in it and want to brand-match whatever is in the crankcase.
I agree with those who have said that it is important to take some time to establish the weaknesses of a particular vehicle so that these can be prevented from developing into emergencies over the course of a lengthy roadtrip. If the car has a known disposition to burn oil, for example, it is important to establish the rate and get a sense of how that fluctuates with engine RPM (the Saturn, for example, burns oil at about 1200 MPQ if the cruise control is locked at 65, which in top gear is about 2700 RPM). Meanwhile, if there is any indication one of the four tires has a slow puncture (caused by, e.g., a sheared-off nail whose tip just barely pokes the inside) or a bead leak, that should be resolved prior to departure.
I am not a fan of minutely adjusting tire pressures over the course of a long roadtrip to compensate for temperature or altitude differences. When I have tried this, I have observed no real difference in handling, but using battery power to operate an air compressor is a good way to age a car's charging system to the point on-road failure becomes likely. I often go months without checking tire pressures at all, and when I have to use a compressor to adjust tire pressures, I first measure the pressures with the car garaged (to eliminate differential heating due to the sun as a cause of error), and run the compressor off wall current.
As for on-road oil changes, I think it depends largely on the engine and the oil used whether those are necessary or advantageous. A turbo or an engine with known design infirmities may demand more strict compliance with oil change intervals; a proven robust normally-aspirated design with good oil temperature management should be able to "skip" a change on a long roadtrip if it is running on a Walmart synthetic (by which I mean not Walmart generic, but rather any mass-market full synthetic retailing at the $20-$28 per five-quart jug price point). In a normally-aspirated Toyota V6, for example, Pennzoil Platinum 5W-30 (marketed as "one of the cleanest oils ever" largely on the strength of its high merit score on the Sequence IIIG piston deposit test for the ILSAC GF-5 rating) is rock-solid shear-stable out to about 10,000 miles of largely highway service, at which point the acid buffering is more or less exhausted (TBN of 1).
I prefer to do my own oil changes because, aside from the odd driveway drip, I can count on myself not to screw them up. While it is possible to bring your own oil, filter, and drain plug washer to an iffy-lube shop with a request that they be used in lieu of unbranded oil out of the gun and a Mighty Auto Parts filter, it takes a lot of checking and supervision to be sure nothing else is messed up as part of (e.g.) an all-points inspection. It is also all but impossible to prevent the drain bolt and filter from being gorillaed into place if that is how they roll.
