選ぶ and 比べる: comparison and selection
Distinguish examining differences from choosing an option.
Differences between options
比べる (くらべる) means comparing two or more things. 「二つの店の値段を比べました」 says that the speaker compared prices at two shops, without stating where they bought anything.
「去年と比べて高くなりました」 means that the price has risen compared with last year. A comparison can involve states at different times, not just two objects.
The selected item
選ぶ (えらぶ) means choosing among possibilities. 「軽い鞄を選びました」 says that the speaker chose a light bag. を marks the chosen item, but selection does not itself mean payment is complete.
「三つの中から一つ選んでください」 asks someone to select one out of three. 中から marks the pool of options and 一つ the number to choose.
Sequence and criteria
「値段を比べてから、鞄を選びました」 describes comparing prices and then selecting a bag. Comparing prices does not establish that the cheapest option was chosen; retain only the stated criterion.
「比べずに選びました」 means choosing without comparing. Even though comparison often precedes selection, 選ぶ does not inherently include a completed comparison.
Does 「まだ選んでいません」 mean no comparison has been made either?
Show the answer and why
No. It says that no choice has been made yet. Comparison may already have taken place.