I have been in Europe many times, but never in Portugal.
This coming Fall I will submit to a medical intervention and to celebrate after my long recuperation, I decided to visit Portugal for 3 to 4 weeks sometimes in 2015.
For those who have been there, what would be the best period? Is it better to begin my trip in mid-April or in mid-September? Those are the 2 periods I am now planning on (although I am very fexible).
I will be 62 years old and interested in architecture, music, food, wine and arts.
Thanks

Anytime is good.
The food, wine, arts and architecture will not go anywhere.
There are some differences, though. Mid-April VS Mid-September there are weather differences, of course. September and July usually compete for the second month where most tourists are travelling around (national and international) the country. April has the lowest numbers of the high-season. That's another difference too.
I think both are good times...fewer tourists in April for sure,but probably worse weather (colder,and more rain).

Since you mention you are flexible and since we seem to agree that mid-April is a tad too early; why not sometime in May or (first half of) June ? Ideal.