I've just found
RENTALIA a very good portal for
holiday lets Rentalia - Holiday rentals. Self catering holiday homes, villas and apartments
They are from the same group as idealista.com (which you may already know as they are the biggest portal for homes for sale & rent) and it's a european company with headquarters in Madrid.
This portal is still relatively new and may not have as many listings as the one you want to avoid.
If you intend to visit different areas of Portugal and spend a few days in each one to explore, the chain of youth hostels is quite good for basic inexpensive rooms. They have
double and twin rooms with own bathrooms, and kitchen for shared use. Some have small appartments too, fully equipped. Open to all ages, not just the youth, and from October the youngsters are all at school, so the hostels are frequented by grown-ups. You may need to get a membership card in your country of residence but it's very cheap and valid for 1 year.
Check site here:
Hostels
Note: The listings of holiday lets registered in each municipality I mentioned above are not very easy to find, because each municipality lists them in their own way and in portuguese, and most only show addresses with no contact number. I think the owners nowadays prefer to get their bookings through portals rather than to deal with bookings & phone calls themselves. If you tell me which area(s) you are interested in, I'll try to send you the listings / webpage(s) for that area, as they don't have listings for the whole country.