The casual term for "toy store" is おもちゃ屋【や】. I believe most children first learn this word around the age of three or four, before learning hiragana. 玩具店【がんぐてん】 is the business term for the same concept, and this is something people learn after they become teenagers. We rarely say おもちゃてん or がんぐや. I have never heard おもちゃみせ.
The jukujikun reading of 玩具 is indeed おもちゃ, but this reading is no longer common outside of old or stiff novels. Today, おもちゃ is usually written in hiragana alone. If you see 玩具 used without furigana in a modern text, such as a news article, you can assume that simple on-reading (がんぐ) is expected.
EDIT: Here are hit counts on BCCWJ:
- おもちゃ屋: 41 (many are from recent blog articles)
- 玩具店: 21 (many are related to business)
- 玩具屋: 17 (most are from novels written by authors born before the 1960's, so I suppose おもちゃや is the intended reading)
- おもちゃ店: 0