Madrid in May

[trg7]

Hi all!
I fly into Madrid to begin a 6 month adventure across southern Europe ending with an everest hike in Nepal.
I'm wondering about the hostel situation in madrid and how to get "downtown" from the airport. In my previous backpacking experience, I know I've been able to walk off a plane and find hostel representers competing and eagerly awaiting backpackers to whisk you away to their hostel. I'm wondering if this will be the situation in Madrid? or do I need to make advanced plans and reservations, and organize transportation? How far is the Madrid airport from downtown and hostel central area? My flight gets in around 7:30am, and I'm sure I'll be anxious to shower up and check out my surroundings
Any suggestions on a hostel in Madrid, and what type of prices to expect this time of year? And lastly, what direction do you suggest I go from Madrid, as I have 1-2 months to explore spain, portugal, and morocco.
thanks for any and all input!!!