Advice from a musician!
I wouldn't recommend any earlier than 4yrs old, although 3.5yrs may be ok if they're and 'old' 3.5 (ie they're already at nursery etc).
I doubt you'll find any decent teacher who'll accept them for lessons if you don't have ANYTHING to practice on at home - because it's all very well having 3 or 4 lessons to see how they cope - you'll see how they find lessons - but you won't be able to gauge how much they're going to enjoy it and improve if they can't practice at home.
If you 'really' can't afford a piano (no a keyboard - unless it's got the full 88 keys and is touch sensitive won't do!) even a £50 2nd hand one then perhaps you could ask at your local church (if you go to one) if you're lucky they met let you in for her to practice a couple of times a week.
For children up to about 8 or 9 yrs old 1/2hr lesson once a week is usually enough, perhaps up to 45 minutes for older ones - or if they're 'really' into it.
As for the reading music, apart from the Suzuki method, most ways of learning DO include reading music, although there are a LOT of excellent books out there which teach the 'music' reading by the way of shapes and colours (so if your child can recognise shapes and colours they'll be able to learn).
Have a good look around for a teacher - and don't just pick one because they're got lots of qualifications, you'll find lots of advance piano students (grade 6 or 7 plus) make excellent teachers, especially if your child only wants to learn for fun - ie without working towards grades.
anymore advice - just ask!