Generally speaking, lighting Chanukah candles is more time sensitive and mikva’ot are open until relatively late, so you should ideally light candles at home and then immerse afterwards. However, if there is some logistical problem with this, you can immerse first (as early as you can) and then light as soon as you return home.
You can prepare as usual for immersion, though you will likely find that performing more of the preparations during the day can take pressure off the night.
Chanukah sameach! Please write back with any further questions.