Our first trip here to Panama in 2011 we purchased a sim for our iPad2 (with cellular data service available on it), and pre-paid a data plan which allowed us to travel all over Panama using online map services (Google maps, etc). We also purchased a cheapy Panama cell phone and purchased pre-paid (pre-pago) minutes on it. Monthly accounts can be activated if desired like the US but we use pre-pay.
Used same again in 2012 when arriving in Panama for 3 1/2 months. And when returning full time to Panama in June 2013, I bought a sim for my iPhone 4S, using a pre-paid phone service, and a monthly data plan. With the hotspot feature on it we can create our own WiFi network' and connect our iPad2 to it, for maps and lookups, or use same on the iPhone wherever we are. My wife still uses the original Panama cell phone. Guess I'm the techy one!
The data plans are pretty similar across the provider companies.....about $15 per month....don't remember the actual download capacity monthly, but we've never exceeded it. However the coverage areas do vary by company....some stronger in certain areas than others.
We have 'FaceTime' on our Apple devices which gives us video phone contact with most of our family for free over internet... and/or cell service which we have never needed to do.
We also use Skype to make phone calls to the US, like business offices, non-family, etc. at 2 or 3 cents a minute. Free in some cases if the call receiver has a Skype account.
Be aware if bringing a cell phone from the US here to Panama for use. The system does not work with CDMA systems (Verizon), but GSM like AT&T. Some of the really new US phones may have dual system usage, but be sure to check. The AT&T phone will accept a Panama sim card which will work for phone service, and if the data plan active will give online availability either thru WiFi or cell service depending on network connections available.
We are in the Boquete area. We used Claro nationwide for maps the first trip with no issues. We have used Digicel for our original Panama phone. And I have service from +Movil now for the data plan & pre-paid phone on the iPhone. It is best to have a local office available for service unless you're fluent in Spanish on a phone. However, most companies offer online payments to 'recharge' (recarga) your phone minutes, and stores offer cards in various values to add minutes to a phone for most companies. And there is another (actually several) online companies which offer 'outsider' online payments to cell phone companies. We use... www.ezetop.com ...which recharges phones all over the Carribean and maybe more. Verify use for your selected phone service provider before using.
Another convenient and helpful map data service choice for Panama is WAZE.com (Ways). Its available in the US, and works in Panama as well. Its maps are pretty current as local users can provide road changes, traffic reports, police camera locations, accidents, slow traffic areas, etc. Free program with many options. If new to Panama, just know street signs are virtually non-existant. There are realistically NO ADDRESSES, as there is no postal delivery service in most or all of the country. So navigation can be important, especially to 'newbies'. (Please don't think of driving in Panama City...use a driver/taxi).
In short, you WILL want a cell phone, and probably will not need a land line. Its much easier if you might change residence location.