1. Travel health insurance
If you are an EU national and travel inside Europe you have emergency medial care covered. But make sure you have the insurance at hand if you live your country and go towards a more exotic destination.
I would advise to spend some time searching for and offer on an international/well-established insurance company that has a strong presence both on your country and on the one you are visiting.
That's more or less necessary spending on where you go, if you plan to rent a new apartment for a while or you just go into the unknown bedbugs are a possible hazard.
Using a bio-insecticide would be best as you will be eco-friendly and it would not raise any eyebrows when you cross a border or something.
I would recommend something like EcoRaider to make sure the product you're using is 100% safe for humans and pets.
Take good care of your money, have enough available for the unknown that might happen especially if you are planning a trip off the beating track and feeling adventurous.
A good idea would be to have a friend or family which can easily send you some cash using Western Union or similar like making a quick deposit on your card.
A lot of places still have cash as king and please keep that in mind or at least check that your credit card will be 100% accepted.
If you are going into a remote location, no Internet or such it would be nice to have at hand the phone number for the local embassy in case of an emergency.