The colony expansion rush is my favorite part as well. There's tons of strategy there: grab the distant but juicy class 16 you may not be able to protect (or even reach before somone beats you to it), or claim the nearby class 7 before someone else does and you have to share your system with them?
But if you don't like it, there are some ways to make it more convenient. Colony ships won't search out colonizable planets for you, but the way GC2 is set up, you really wouldn't want that anyway: colony ships are too slow and have very little sensor range so they'd be terrible for finding good planets.
What you want to do is take your scout ship, double-click on it (or press the details button), and select "auto-explore". This will make your scout search out all the unexplored areas on the map for you. Design and build a few more scouts if you can afford them and set those to auto-explore also.
As new planets are uncovered, they will be added to the planets list you can bring up with the button on the left of the bottom row (or maybe F1 as well). Once you bring up the list of planets, click on the "unowned" tab, and it will give you a list of every planet not currently owned by anyone, sorted by quality. Now, select your colony ship and pick a planet on the unowned list with a quality > 0. This centers the map on the planet. If you like the look of it, right click on the planet to send your colony ship there. Lather, rinse, repeat.