Take loop 335 around Amarillo to I-40.
Left on I-40. A few miles to the west is Cadillac Ranch. Pretty cool place to take a few pics and spray paint some old Caddys.
Keep on I-40 to Bushland (5-6 miles) Rt on 2381. Stay on 2381 to Tascosa. It is single lane but rural country roads so not much in the way of traffic.
Rt at Tascosa (Hwy 385) to Hartley where it joins with Hwy 87.
If you do decide on going thru Amarillo, the downtown area gets congested so keep your head on a swivel and watch out for the other drivers and for your exits.
There is a lot of agriculture in the panhandle so the fuel stations are use to dealing with semi's so your trailer won't be a problem.
FYI. Watch out for the cattle haulers. Those guys are CRAZY and only know 2 speeds, stopped and 100 mph. I spent about 10 years in Amarillo and there's nothing worse than having a cattle truck in your rear view mirror. I think they like to drive faster when there is snow/ice on the ground.