여 in 고려하여 is a case of the -아/어/여서 connective ending of a verb or adjective. It is one of the most common verb ending forms and creates a sense of "and then" or "because", i.e. you do one thing first and then another based on the result of it, or one thing becomes the cause of what follows. It can be 아서, 어서, or 여서 depending on the syllable before it: 여 after 하(of 하다 - as in your 고려하다), 아 after a syllable with ㅗ or ㅏ in it, and 어 for all others. And 서 can be dropped in many cases as in your example. So 방의 목적을 고려하여(서) 선택하는 것이 좋다 means "It is best to consider the room's purpose and select (the wallpaper) based on that", or "It is best to consider the room's purpose when picking the wallpaper for it". (Also note that 하여서 is most often shortened to 해서, so 고려해서 is more common than 고려하여서)