「私{わたし}は押{お}し入{い}れの奥{おく}から、夏{なつ}の洋服{ようふく}を出{だ}して、かばんにいっぱい入{い}れて出{で}かけることにしました。」
Your translation of that is:
"Out of the clothes in the closet, I took the Western-style summer clothes out, I put them in the bag (full), then I took them out."
Your TL obviously makes little sense. Why would one put clothes in a bag and (immediately) take them out?
「出{で}かける」 means "to go out", "to leave home", etc.
「出{だ}す」 means "to take something out", which you translated correctly.
Thus, it looks like someone is taking a trip, doesn't it?
Moving on to 「ことにする」.
This expression has been discussed many times before so I will be brief.
「Verb + ことにする」
means:
"to decide to [Verb]"
You will encounter this expression over and over again as long as you study Japanese.
My own TL:
"I decided to take my summer clothes out of the closet, stuff my bag with them and leave home."
(「洋服」 surely means "Western-style clothes" literally, but because what 99% of Japanese people wear on a daily basis are such clothes, the word just means "clothes" to us.)