Traveling with luggage in Machu Picchu region and avoiding altitude sickness

We have a trip ahead in South America that includes about 4 days in Cusco - Machu Picchu region. The main purpose of this part is obviously to see Machu Picchu, a bit of the Sacred Valley, catch a glimpse of Cusco and possibly one more place in that region, maybe Tipon.

We are traveling to Cusco by plane from practically zero altitude, so one of the major things to consider is minimizing the risk of altitude sickness when planning the itinerary. The scheduled arrival time is around 10 am in the morning, but this is after several flight connections. Should something go wrong and we miss a flight on the way, we might not make it to Cusco till the evening, which further imposes risks on the decision about the date that we should buy Machu Picchu tickets for, since those are bought in advance and cannot be modified easily.

As you can guess, the question is how to plan these 4 days. Since Cusco is very high (3400 meters), I don't consider it an option to sleep there the first night. Better would be Ollantaytambo (~2800 m) or even Aguas Calientes (~2000 m) in case we can make it there.

The second issue to consider is that each one of us is traveling with a luggage of 12-15 kg and a small backpack of 3-4 kg. Obviously we would like to spend as little time without access to our luggages as possible, preferably no nights at all.

Traveling to Aguas Calientes with the luggage can be problematic, especially since we'll be there in the high season, although still possible. In case we are willing to pay extra for that option, how can this be arranged, and how much extra will that be on top of the regular train ticket prices? In this case we would spend the first two nights in Aguas Calientes, see Machu Picchu on day two, and the third day heading back to Ollantaytambo and probably to Cusco the fourth day.

If that's too risky or simply doesn't work in the high season, it seems that staying in Ollantaytambo the first night and leaving the luggage there is the best option. We would go see a bit of the Sacred Valley the second day, sleep in Aguas Calientes, then see Machu Picchu on day three, head back to Ollantaytambo in the evening to meet our luggage again and sleep there, then head to Cusco on day four. The obvious disadvantage of this alternative is that we are spending one night without the luggage, we should find a safe place to store it in Ollantaytambo for maybe over 36 hours (where?), and that we are spending the first night at around 2800 meters instead of the appealing 2000 meters option.

This is what I could come up with so far, but all different itinerary ideas are also welcome, as long as they match our restrictions and preferences. Lots of people on the internet write about how less is more and you should try to travel without a luggage and everything, but it will be a long and exhausting journey and this is really not what we want. We're not traveling on extremely tight budget, meaning that we are alright with taking trains as such, but only as long as the prices are reasonable. This means that we don't want to pay a hundred dollars just to take the luggages with us on the train, finances are still a part of the equation as it is to most people on SE.

Surprisingly, out of the several countries that we are planning to visit, this region has been the toughest to plan. I hope to shape the remaining part with your feedback and ideas. Thanks in advance.

Edit: please note that the main question is not how to deal with the altitude sickness, rather what's the best route plan under very common restrictions such as traveling with a luggage and keeping in mind the altitude sickness.