Time travel is a dangerous adventure. Good luck though.
To build the machine I would make a pod out of Aluminium, its light and can be easily made into any shape. I would paint the outside in Lead paint to keep out the radiation.
As time travel is thought to occur in a very quick amount of, relative, time - the time it takes to travel from one point in time to another - I don't think an air supply would be of a great concern. Take a portable air tank if you're worried. I don't think weight would be a factor either, in space and time there is no factors of weight only gravity. And if you are travelling through time you have to realise that the space will change too. You'd have to travel in time to the stame day in the previous or future year, otherwise the Earth may not be there to meet you. .... Same time too, if you think about it or your machine may end up in the wall. - There's a lot of math here you need to calculate.
If you want to change the past or future you must ensure you do not meet yourself. You can encounter other people but if you meet yourself you will create a paradox and NO ONE can say what will happen... you may distroy time itself. Who knows. To change anything you have to influence others around the former or later you. -- But you can't judge your outcome until you get back to your own time... and who's to say it will be any better?? - You may have to travel continuously and never be happy, just to get everything right.
So don't try to change everything, just the big things. Nothing is perfect.