Will you be doing extensive outdoor activity like hiking or going into mountains? If not, then rain pants are overkill. Regular pants that dry reasonably quickly will be fine for walking around towns or light hiking.
Also nothing in the weather forecast or averages for those towns indicates than an average person would want a winter type hat or mittens. Or a fleece coat. A sweatshirt and raincoat would be fine. Make sure the sweatshirt can go under the rain coat in case of cold rain.
The overnight lows are in the 50s. To me that’s sweatshirt, pants, no hat weather.
My advice - aim more towards summer. By June it’s much more likely to be hot and you’d want a sun hat and breathable fabric.
Source: was in Lisbon in March. Highs in the 50s-60s, plenty of rain some days. Did fine with a raincoat, jeans or light pants, and a variety of shirts, some long sleeve, some short sleeve, some worn with cardigans/sweaters.
Have been in Spain in May/June and was more likely to need a swimsuit than a sweatshirt, let alone mittens!