Based on moving between Panamá and the USA several times through the years, with our entire family, I can assure you this:
Pack just the memories you treasure the most.
Everything else, stays, specially all electronics, kitchen stuff, or furniture.
Bring favorite movies, if you wish, and books in English.
The reason for this is that you can get everything and anything in Panamá, at very low, ridiculous prices, from a pack of needles, to the most modern car. And, you will save a lot of money. There are several malls that will surprise you with what you can get, and at the prices you have never experienced.
For example, the Albrook, El Dorado and Metro, in the city of Panamá and the Westland in Arraiján, three malls in Coronado (Pacific beach areas, about an hour from the city of Panamá) are very well known for selling everything, have great food courts and restaurants at envious prices.
There is the Multi Plaza Mall in the city, which carries every single upscale brand of the very best fashion from Europe, US and around the world, so, if you are in a budget, or not, you will find here everything you are looking for.
And if your location is Boquete, or some other town in the "interior" (countryside), there are shopping centers, and small malls in all of them, like in Chitré, Chorrera, Penonomé, David, among others
Remember that items are imported from all over the world to Panamá, which is the reason why merchandise can be offered at very low prices. You just need time to look everything, and you will have a very difficult time choosing because you will want to buy everything.
And if you go to Chitré or El Valle, you can buy beautiful art and crafts, "molas" and hammocks at an enviable prices.
Coincidentally, I just received an ad from Wal-Mart in the US offering a hammock with metal legs at $128.00 on clearance. Well, in Panamá, you can buy a way better one for between $50.00 and $85.00. There is a store by the Interamericana Highway that, while you drive to the "interior", you can stop and buy one, or in El Valle.
I know people who brought by a full 40-foot container, and have been ruined because they either couldn’t fit all their items into their new house, or didn´t get the house they were looking for on time.
So, here’s some good advice: Bring no more than 10 boxes with all your belongings. It’s easy to manage, inexpensive, and practical. No winter clothes, no heavy things.