Why did Gon and Killua tag along with Kite in the first place?

Yeah basically what you said + they were interested in Kite's work and were just excited to help out (it's clear in chapter 186 when you see them eagerly show curiosity and want to assist). Then the whole ant thing came up and they wanted to help further, both because they were confident they could assist and also because they want to get stronger and all that. IMO that's why in chapter 198 after they leave Kite Killua says to himself that they were too complacent and overconfident in their powers, they underestimated the threat and mission.

After that the motives change once they have to leave Kite, since then it got personal both in terms of saving Kite but also Killua and Gon wanted to confront their own weaknesses and grow stronger.

/r/HunterXHunter Thread