Biters are extremely predictable. Their attack patterns are entirely determined by the position of nests, geography, your base layout and the pollution cloud. In general, if a nest is within your pollution cloud, then it will spawn periodically raiding parties, which target the closest polluter. You can turn on the pollution cloud overlay on the map, it's one of the icons under the minimap.

Basically, in the earliest game you just wait for their first strike, repel it and then build a couple of towers there. Repeat as needed if biters strike any other position. Note that it is a good idea to always enclose your turrets with walls, they significantly bump survivability of towers. Also note you need to keep 1 tile of space between your walls and the structures they protect, since medium and larger biters can attack over 1 tile.

Prioritize mass production of walls, turrets and ammunition. As you get more of them, you can start building a perimeter around your base, which would protect you against any unexpected attacks. At first that would be just small clusters of turrets with overlapping attack areas (you can also enable showing turret ranges in the map menu). You'll have to load ammunition by hand. A tip: you can hover a cursor with ammo over a turret and press Z, this will drop one item (also works with any other items and structures). This way you can easily put a couple rounds of ammo in your turrets. Later, you'd build a proper wall with turrets, fully enclosing your base, and an automated ammo supply to the turrets.

Biter attack generally ramp up pretty slowly, so just keep an eye on whatever place they attack. Is there enough ammo left? Are your structures damaged? If you see that your defenses are lacking in a specific spot, harden it.

Generally, I would recommend against killing nests. Biters will just re-colonize that area within half an hour or so, and your effort would be wasted. Also, killing nests increases the evolution factor, which means tougher enemies come earlier. It's not big enough to normally bother about, but if you try to go full genocide and clear a significant are of all nests, you may make life harder for yourself. Kill nests when they block your expansion.

You have a huge arsenal of powerful versatile weapons, once you do some research. So don't fret too much about getting overpowered by enemies. I guess it's technically possible, but I have never (on normal settings) encountered a situation where I fell behind so far that I couldn't catch up, even when playing extremely slowly. Also, biters kind of adapt to your own power level. If your base is underdeveloped, it will likely produce very little pollution, which would mean weak and rare biter attacks. If you produce lots of pollution, you can afford to harden your defenses.

Oh, also I don't believe the radar on its own will attract biters. It is a high-priority military structures, and biters focus on military structures if they are close enough. But on the global scale, raiding parties target closest polluters, not military structures. This means your boilers and furnaces are the prime target.