Welcome, Jakob.
As a starting point I suggest you reading the Best Practices advice (
http://jmeter.apache.org/usermanual/best-practices.html ).
At first, before capturing the script, add an HTTP Request Defaults
configuration component and fill in the fields host, port, HTTP
implementation, protocol and content encoding.
Before capturing, add as many Test Plan variables as the hosts you are
testing against (I suppose you are already doing this).
The first will ensure that any HTTP request captured by JMeter proxy, that
have the same parameters, will follow the defaults (fields inside HTTP
Request sampler will be left blank).
The second will help you to parameterize some of the Request Headers
parameters. Ex.: Host and Referer parameters.
After capturing you could change Host field in HTTP Request defaults with a
Test Plan variable.
Test Plan variables that are subject to change should have their values
defined like this: ${__P(myHost1,my.host1.com)}
myHost1 = parameter passed on command line: jmeter -n -t myTestPlan.jmx
-JmyHost1=my.alternative.host
my.host1.com = default variable value if myHost1 parameter is not passed
