Should I invest
in my new country or my old country?
What should
I do with my savings?

Only my opinion, I am not a financial consultant, but
unless you plan on spending a long time overseas -
invest in your home country.
There will be times when you might become aware of
unusual or special opportunities for investment in your
new country.
I would advise staying away from them
unless you have lived there for several years and have a
strong understanding of the financial and legal system
where you are.
Most of us don't have that
understanding, and foreigners are often fair game for a
good fleecing.
Yes, you can always check websites that offer global
financing tips like the popular
Motley Fool, but nothing beats first-hand experience
and knowledge. Your researching can only take you so
far, when it comes right down to the nitty-gritty detail
of investing, you're better of doing damage on a
territory you're familiar with and have connections on.
Long-Term Investing
If
you plan to live in a certain country for the rest of
your life and perhaps to retire there, then, and only
then, should you consider investing in that country.
And first, be sure to listen to the old "war stories" of
people who have gone down that path before. You work
hard for your money, be careful not to blow it on
something you have not researched carefully.
The
Discussion Boards
I
read people talking about investments on the TEFL
discussion boards - and they often, sadly, have no idea
what they are talking about. I have an MBA, have
invested carefully for thirty years in real estate and
in the stock market, yet often hear 21-year-olds tell me
which way the US dollar is going to move against the
Korean won.
Flip a coin - even experienced traders with
years of Wall Street experience rarely really know. Get
your investment advice from your own personal research,
pay a professional for good research, or don't invest.
Don't get your investment advice from English teachers.
Just my opinion.