if you want to avoid steep climbs then i'd recommend:
I-8 east to I-10 east
I-10 east to I-20 north
I-20 north to I-30 north at Dallas/Ft. Worth
I-30 north to I-40 north at Little Rock
I-40 north to I-55 north at Memphis
this will avoid major climbs but you'll have some cities to deal with the worst (IMO) is Dallas/Ft. Worth. If you want to avoid DFW then take I-10 east to NM SR26 at Deming. Follow that to I-25 at Hatch and then follow I-25 north to Albuquerque where you'll pick up I-40 east. there will be one decent climb on I-40 a few miles east of I-25 but after that it's basically all gradual downhill to Illinois.
at Oklahoma City you'll want I-44 east. I-44 is a tollway between OK City and Tulsa and again between Tulsa and the MO state line. if you want to avoid the tolls then stay on I-40 at OK City to I-55 at Memphis.
the advice to be sure that the MH is road worthy is excellent and should not be discounted. me? my main concerns would be the tires, brakes, shocks...basically the suspension system. also fluids...oil, grease.
other than freak spring storms your weather should be fine. good luck.
