It's great to concentrate on a single airline if you will fly enough to earn elite status on that carrier. If not, it's probably unwise to collect all your miles in one FFP. Sometimes AA will have low-tier (cheap) award seats available when you want to redeem your miles, and UA will not. But sometimes, it's the other way around. And if you won't fly enough in one year to earn status, then, depending on your likely award redemptions, you might be better off collecting miles in a completely different program! For example, you can credit an AA flight to British Airways, Iberia, Japan Air Lines, or any oneworld carrier. And UA flights can be credited to any Star Alliance carrier. What's the benefit of crediting your miles to a carrier other than the one you are actually flying? Each carrier has different redemption rates, rules, fees, etc. For example, later this month, I am flying a four-segment roundtrip on AA where the total flight distance is between 600 and 1,000 miles. The normal redemption rate for that trip would be 25,000 AA miles, 30,000 BA Avios, or just 12,000 Iberia Avios. I booked this award ticket with Iberia Avios.
Whether you should collect frequent-renter points, hotel points, or airline miles from your car rentals (many programs give you a choice) will depend, in part, on how long each rental lasts. The calculation will vary depending on whether you'll be booking two seven-day rentals, vs. seven two-day rentals.
Give us a little more information re: your likely frequent-flyer redemptions (routes, class of service, season) and we can probably provide better recommendations.