Visited MP some years ago, so no experience with the new system. What circuit you do depends largely on a) your physical condition and b) what you are truly interested in.

Most of the walking around the Citadel itself is not very physically challenging, lots of uneven stone steps, but on predominantly flat, firm surfaces (some gravelly/dirt paths). But highly technical hiking boots/shoes or expensive walking shoes are not required. Normal sturdy walking shoes are fine - I witnessed more than a few young kids (locals!) wearing flip flops (highly discouraged - especially because it is slippery everywhere when wet).

The problem is that it is at altitude, about 2400 meters (~8,000 ft) - so folks used to living close to sea-level get winded much more easily than they expect. So without knowing your age and physical condition, but since you already seem aware of the conditions and are going anyway, I am going to assume you are in typical, reasonable, normal shape (you don't get winded climbing one flight of stairs in a house/office building) which means you should be able to do all circuits (with caveats for Huayna Picchu - read on).

Huayna Picchu is a technical climb and you do need to be good shape - it is steep, very few handrails (and not where you really want them) and has lots of uneven size steps - few are the same size as stairs at home. And you do need good walking shoes/light hiking boots for that, especially since you are going when it is guaranteed to be wet. Unless you are a professional athlete you will definitely feel the "burn" in your thighs and hamstrings - especially on the way down. But the views of the citadel from HP is something few people experience... (less than 10% of daily visitors are even permitted to climb HP). Lots of portions where there are steep dropoffs with no handrails and very narrow paths - this is not a hike for anyone who suffers from vertigo.

Best kept secret: hike Huchuy Picchu - it is the small "mountain" next to HP - only 100 meters. Almost no-one hikes this, it is an easy walk, and gives you awesome views from above the Citadel without the challenge of HP. It does require the same extra ticket as for HP.

On the other side of the Citadel, the trail to Intipunku (the Sun Gate) is doable by just about everyone in normal reasonable condition. Again, good walking shoes are recommended - uneven stone paths, roots, some unpaved areas - all of which are slippery in the wet. But not at all technical.

So, which circuit? Assuming physical condition is not an issue - then it comes back to, "what is purpose of your visit?" If it is for bucket list hikes, then do any of the C1 or C3 routes including HP. If it is to see and learn about the culture, history and magic of this mysterious place, then the C2 routes are the thing because the focus is the Citadel.

The other question is what time to enter. Even though the entire place is capacity and timed-entry controlled, it still gets crowded. So, my recommendation (which I learned from professional MP tour-guides) is to do the C2 routes in the afternoon of your first day, then do HP or Intipunku early morning of your second day. This is because most tourists (and the school groups) get there first thing in the morning and get tired, hungry and leave by 2pm. This means it is MUCH less crowded in the afternoon making it much more relaxed and enjoyable. The Citadel takes about 2-3 hours, so get a 1pm entry.

Have fun, it is a most magical place!