WiFi security question

I am considering a long term rental in a place close to the beach in Mexico. The WiFi in the building serves at least one entire floor, maybe more. The assigned password is horrible, as in 1, 2, 3, 4, 5,...that type! The building is in a very busy area, all in all, about the same security you would get at a Starbucks, I would say.
I don't really care if my browsing history is seen, I've nothing to hide and don't do anything even remotely illegal on the internet, (or anywhere else for that matter).
That said, I DO all of my banking/investing over the internet...ALL of it. The sites I need to connect to, a bank and an on-line investing service, are of course secure and password protected.
So, is this risky in terms of my accounts being somehow hacked? If yes, what if anything could I do about this to keep myself safe? Or, should I not even consider this arrangement as a long term condition? The accounts I refer to do in fact represent my entire life's savings and investments, and I would be in a foreign nation, if that is of any relevance. (But, the beach is only a block away!)

 

When in Mexico, I do use Private Internet Access as a VPN. Gets me around all the annoying referrals to Mexican sites. I know you can get google and yahoo US, but it's a bit of a hassle, especially with yahoo, people down here seem to be having issues with it. But, using the VPN fixes that, also allowing me to use my Time Warner account and access to some other sites that otherwise don't work.
But I don't know if this adds a bit to my security??
Obviously my access to my bank and investments have security measures built in. Although with the investment site, my google chrome is set up to remember the name and password and gets me right in. Is this a weakness? Should I disable the "remember log-in" feature? My lappy is of course password protected, upon shut down and put to sleep. So if it is ripped off, I don't think anyone could use it to get to my accounts.
But my main concern with all this is still the shared wifi connection. A personal connection is not offered at this place I am considering, and internet access for banking and such is a must have for me.
Just trying to figure out if this is a deal killer before I sign any lease agreement! Kinda sounds like it might be??? confused:confused