Mmmh... are you going to work for the Champalimaud Centre for the Unknown?
If you are, it’s good to see some brains coming in, instead of going out.
On the website of the Champalimaud Centre they say there is a bus from Algés Train Station directly to the center. This Train Station links “Cais do Sodré” (Lisbon) with “Cascais” and there are several buses departing from here and a tram do Lisbon.
You are very near of an upscale neigburhood (Restelo) where a lot of embassies are based, Belem neighborhood probably is a little bit more cheap (it has culture which ends up of being touristic – Centro Cultural de Belém; Mosteiros dos Jerónimos; etc).
Even cheaper: Algés neighborhood (not so pretty has the previous two) or Ajuda neighborhood.
You can also check Miraflores neighborhood (small skyscrapers but still cute area) or if you like sports Linda-a-Velha (Alto de Santa Catarina) neighborhood or Cruz-Quebrada neighborhood (the last one have upscale houses with great ocean views but also cheaper houses on the lower part of the neighborhood) are close to “Estadio Nacional”
In terms of transport systems near the train stations of Algés or Belém would be probably the best areas to move around quicker to other parts of Lisbon (Belem has a boat connection).
And on foot, the closest area of Belém Tower is Pedrouços neighborhood just right on the other side of the railway just before entering Restelo neighborhood going uphill.
Are you planing to have a car? How many rooms to you want your house to have? It's hard to answer in terms of cost and culture if you don't specify more what you are looking for
