The Energy Research and Development Administration yesterday chose Golden, Colo, as the site for its Solar Energy Research Institute, and selected the Midwest Research Institute of Kansas City, Mo., to operate it.

The selection of Golden and Midwest Research ends almost a year of political infighting in which 16 states and 19 organizations vied with one another for the institute, which is understood to be the first of its kind in the world.

For its first year of operation, the Solar Energy Research Institure will have a bedget of about $5 million and a staff of about 60. By 1982, the budget is expected to climb to $20 million a year and the staff to be more than 200.

An ERDA spokesman said the new institute will not direct alli solar research, and that such research will be coordinated by ERDA here. The institute's budget will be a fraction of the $305 million ERDA has asked for in the coming fiscal year to do solar energy research across the country, the spokesman said.

Golden is west of Denver in the foothills of the Rocky Mountains. The ERDA spokesman said he expects there will also be three regional solar research institutions, one in Boston, a second in Georgia, Florida or Alabama, and a third in Wisconsin, Michigan or Minnesota.