There are two practical routes across the mountains, either I-80 or I-40. There are minor variations along the way but the general routes keep you away from the really tall rocks.
The trip is a situation of look at the current weather and forecast, make a choice of northern route and cooler temperatures or south and generally more benign weather, and go. Chicago to Cheyenne for the northern route or Las Vegas for the southern route - typical midwest flatlander flying - dodge the thunderstorms.
The northern route is follow I-80 across Wyoming and turn left at Salt Lake City, head to Vegas in the big/wide valleys and on to LA. Southern route is just follow I-40 to where yer goin'.
Either route will be bumpy if the winds are high. For the northern route the area around Laramie & Muddy Mountain VOR is usually the worst. Avoid flight directly downwind of the tall rocks. Stay on the ground if winds aloft at your altitude are greater than about 30 knots. Fly early in the day to avoid high winds. For the southern route, the stretch from Las Vegas NM to Albuquerque can be entertaining for a flat land flyer. Sometimes it's best to stay out east to avoid mountain wave in that area. After that the ground elevations are high but no real mountains until California.
For stops along the route you'll want to lean for max power when density altitude exceed about 3,000'. If you don't know how to do that plan on a little time with a local CFI for some high density altitude training. Keep yer gross weight at or below 90% of max gross for the aircraft when operating out of high elevation airports. Avoid flight in the mountainous areas when winds are much higher than about 30 knots at your planned elevation. Do not fly near the rocks when they are obscured by clouds. Do not fly near the rocks when they are obscured by clouds. Did I say that twice? It's sorta important since bumping into rocks while in flight is generally a bad thing. One other thing, that 14,000 ceiling? That's a density altitude thing, not an indicated altitude thing. Every now and then someone forgets that and the local (Denver) news stations get to run a story about little airplanes being dangerous and killing someone or a whole family.
Overall the trip is doable but remember the old saw about time to spare, go by air. Ya gotta be able/willing to stop or divert for weather and/or deal with the inevitable mechanical problems. The SP is a fine aircraft for a solo or 1 pax jaunt. You'll spend a lot more time (thus exposure to weather changes) on the trip than the Mooney or Bo drivers spend but you'll learn more. These long x-c are a great opportunity to exercise the license to learn but ya gotta be patient and willing to say it's time to stop for the day.
