I'm wondering what general fitness would suffice to hike to the base camp of Everest? Does it requires special fitness regime and focus on main body parts like legs and core strength?
I assume you're talking about the south base camp in Nepal, which is the more popular destination. The typical route gains about 8000 feet over 40+ miles, which is really quite gentle, although the net effect of all that altitude is significant.
It's mostly class 1 with some class 2 (rough trail/scrambling), so no technical skills required. Supplies/lodging are readily available, so you wouldn't necessarily need more gear than for any day hike.
Other than the need to acclimatise, it sounds pretty easy, at least from my perspective.
While Patrick's answer here clears many of the points, I would like to make up a few points about warm-up routines and acclimatization.
A few points may sound very specific to you and not really generic at all. For us, Indians, that weather is not really what you can call normal and pleasant, with the gradual (if it is) gain in altitude adding to a wee bit woes like milder headaches.
While assuming that you are already overall prepared physically, make sure that you go for multi-day hikes before you set off to Nepal.
- It should ideally take 12 days (round trip) to get back in Kathmandu. Make sure that you are physically and psychologically (I know you must be) prepared for a 12-day hike if you are not really used to of doing so. I have seen people hauling a 18 kg backpack effortlessly for close to 5 days and then there they loose it later.
- Practice ascends. In India, specifically in the non-Himalayan terrains, people are not really used to the habit of multi-day ascends. They would usually gain height for a day, camp at night and then probably descend the same or the other way down. At EBC, you would gain height for 3 days on a stretch. Need not be worried about, those are awesome planes to gain heights, but be prepared.
- If you don't really pay much attention to warm-up routines here, you can't get away by doing the same there. Get used to with the habits of stretching and other warm-up routines.
- Know your gear. Gear has a lot to do with your overall physical capability. Be it the shoes, or be it the backpack, or whatever. Get familiar with the gear. Sometimes a newer backpack bought specifically for such an expedition is not something that you get used to with on day 1. You might want to consider using the same lot of gear in the region known to you so that you would know what you are taking along. I have had a bad time on field due to a costly backpack that I thought would suit me, it didn't.
- Even on your best day, you would not want to gamble with acclimatization as it is planned. If you haven't given acclimatization a thought, do that. From a month before I was to leave, I was advised to stop/avoid taking Aspirin if I do in case headaches. Up there, you would want to avoid painkillers for silly reason and would definitely want to know whats happening with your body. If you have headaches, you need to know, rather than suppressing it with painkillers.
A very important thing to remember: Many a times overall public health in Kathmandu is a something that you should be really careful about. Do not gamble on Food and Water quality in Kathmandu. A Gastrointestinal infection is as common as a mosquito bite over there.
For the preparedness part of it, you would want be able to check 'Yes' with most of the things below.
- I can haul a 15 kg backpack.
- I am absolutely game for 3 consecutive days of gradual uphill hikes.
- I am absolutely fine with garlic-rich food.
- My trekking schedule during the whole thing is inclusive of the buffer time should I need to delay something by a day.
- I am comfortable at colder weather than I am usually at.
- I am not going to exert myself beyond a certain limit that I feel like this is once in a lifetime shot at it.
Have a safe trek!