First "long" cross country: KRHV to KRDM ADVISE NEEDED

Well after 150hrs and preparing to start my Insrument, Commerical, &
CFI I figured it is time for my first VFR cross country that requires
an actual fuel stop. Flight will take place the last weekend in August
(assuming weather cooperates)

My dad lives in Redmond, OR, so I thought, what a better flight.

I have a few questions, but before I ask them let me give you my stats.

The flight will be in a 2003 C-172 SP. I do not have a mountain
checkout yet, but am planning to get it in the next couple of weeks.
This will be a day VFR flight solo with only my 30lb flight bag and a
duffel bag of clothes

Furthest North I have gone so far is Auburn (KAUN)

Main navigation will be GPS via the KLN94 and MFD in the 172 with a
Garmin 195 as a back-up.

Planned altitude (so far) is 10,500 there and 9,500 back. The track (so
far) is (KRHV) Reid Hill-View to (KTCY) Tracy to( KSAC) Sacramento to
(KRBL) Redbluff ALSO FUEL STOP.

From (KRBL) to (KRDD) Redding. After that I am not sure about west or
east of Shasta. Any input about this?

Whether west or east of Shasta, will end up at (KLMT) Klamath Falls to
(KRMD) Redmond via Hwy 97

Any thoughts, comments, suggestions, experiences I would greatly
appreciate it.

Ok besides your general comments, a few specific questions.

Should I carry oxygen for 10,500ft?

West or east of Shasta?
If I go to the west (following I-5) I will be flying inbetween Mt.
Eddy and Mt. Shasta with about 10miles on each side but with more
possibe airports. If I go to the east of Shasta then I can fly further
from the mountain itself, but have fewer choices of airstrips to use.

In the summer time, which side of Shasta is the leeward side (bad
downdrafts) and which side is the windward side (updrafts)?

Of course part of my planning will include phone calls to the various
airports and talking to local flight instructors. Also flight following
(as coverage permits). Also will be filing a flight plan.

So there is it is folks, any and all useful information is welcome.

Thanks,
Donovan