If you look up 切(せつ), it's actually an adjective meaning 'eager, earnest, kind' (despite these meanings not being listed for the character in my dictionary), and 親 can also mean 'familiarity, intimacy', so 親切 doesn't seem so strange. 屋 also has additional meanings 'shop, seller, dealer', so I think if you do a little bit of research, you can understand the logic to most compounds.
If you get a program like Wakan, you can use the Heisig keyword to look up characters really quickly (works 99/100 times). Otherwise, you can use the old school methods of look up just as easily. The etymology website Yuuichi posted the other week might be useful for understanding strange ones too.
Anybody who's finished Heisig Vol1 might be interested in the Ultimate Japanese deck on the Anki site. It has at least 1 on and 1 kun reading for each jouyou character within 7200+ short example sentences, which makes remembering the readings really easy. If you can get through about 50 or so of these the day you'll be laughing. Never tried Heisig Vol2, but it's hard to imagine anything being as easy as this, while at the same time getting you to remember thousands of words in context.
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Say Hello in Japanese No Matter What the Time of Day
Absolute Beginner Season 1
Learn how to greet someone both formally and informally
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