I find that playing on the highest difficulty will come down to a very narrow point spread, so get used to that high anxiety play. On both missions you need to prioritize conserving your higher scoring units while sniping the buggies and bikes with artillery.
For the first mission I dropped the Space Marines on the bridge with the Thunderhawk on turn 1, and with their remaining movement entrenched on the near side of the bridge, creating a fatal funnel, and cover on the flanks (check your field of fire with one of the icons to make sure you're in a good spot). I moved two Predators up behind the marines on the bridge for support, and one to the left near the forest to cover the northern approach. Once I had that first objective I could take the enemy as they came. I used the Thunderhawk to harass northern / western infantry, and to snipe at bikes when I could - fly in, shoot em up, fly out.
The second mission was more touch and go. What worked for me is to lead with your lasgun infantry and chimeras in one line, with the heavy weapon infantry out of range of ork boyz. Inch this force up while retaining at least one fire action - two is better, but will require you to make a mad dash for the first objective towards the end. Since your force is primarily infantry, you'll want to prioritize killing ork boyz with your infantry and chimeras - use the bombards on the bikes and buggies. Do not discount the thudd guns. They are slow and relatively weak, but shoot at whatever is in range when it comes in to range - if nothing is in range, move them up aggressively. As soon as you feel comfortable, move a chimera or the rhino to grab the objective and keep the enemy from contesting it.
After these missions, when the real game opens up, I shuffled units around quite a bit. I removed the thudd guns and one unit of chimeras from the first battalion and replaced them with the Leman Russ and Basilisks - this is my primary battalion and have been using it for most of my current game. The Tallarn battalion will be pretty weak, so don't use it until you can afford to beef it up later in the campaign. Whichever army you use, do not forget to get AA batteries! Try to conserve your tanks as best you can and get them experienced. Once the gargants start rolling out in the counter attack, you'll want something that can reliably get through the shields and armor.
Have fun!