OP, Listen up.
Anywhere over 2,500m it is possible to get sick. Most people adapt better but most likely you'll notice a change at 4000m if you acclamized the night before. Really geneticly talented poeple can go up to 6000 an be okay but do not count on being that guy.
If you want to do Everest with out any regard to style start running or biking and if the weather is good you'll make it. If you start training now you'll be good for pst monsum season in September. But if anything goes wrong chances are you'll die, be it weather or anything else. I'm not recommending this but it is a possibility.
If you want to get into mountaineering and test the waters first, I'd suggest start climbing and try to tick off mountains at home. With an larger skill set you'll start doing stuff in winter and this is good training for high-alltitude weater. Plus I heard you have no huts up there so you'll be already familar with a tent and camp life when you are on an expedition.
Next go to the Alps and do Mont Blanc. Glacier trevel should be in your skill set by then, if not try to find a group that goes up with an guide. It would be even better if you know somebody that could show you the ropes and you could use as an mentor.
After that it gets costy. Kilimanjaro is about 2000€, Aconcagua 2500€, Elberus can be really cheap. Denali 4000€. All those prices are already very budget-y and don't forget you'll need the gear to go with it. -30°f Bag on Denali, Parka, boots, tent, ...
At last there is Everest. If by that point you are already a guy that is know through out the Norweign Alpine Club because you are so rad and your accents are so sick, consider climbing Everest without an guide company. Other wise pay 10000€ and you'll be some guy in the line in the pic. Also I believe only 52 people summited Everest without O2, so here's something to work for.
>>260520Mah Austrian Nigga (?)