If you are going to run small Transmitters and microcontroller off batteries, its critical to look at the power
consumption of what you are running, otherwise you will be replacing the batteries every week.
This means running the microprocessor in ultra low power consumption mode, and running the transmitter
as infrequently as possible.
For example, the little transmitter you are considering, draws 8 ma when transmitting.
Running this off a 9V battery, if its a small transistor radio type battery will drain the battery in just 12 hours.
Even running the Transmitter for just 1% of total time will drain the battery in just under 2 months.
Its critical to minimise battery consumption which means using the lowest possible supply voltages and keeping the transmitter
on time as low as possible.
Id be looking at running off 3 V which you can get from 2 AA cells in series, using the highest data rate you can manage
and thoroughly understanding issues like manchester coding,CRC error checking, and microcontroller power management.
Also, the frequencies that these small transmitters use , are commonly used by many common household appliances like garage door openers
car entry systems, wireless door alarms, wireless security systems etc so you must be able to recognise your data from everything else thats around.
The better transmitters like the Xbee use 2.4 Ghz and do all the hard work for you, which is one of the reasons they are more expensive.
They also draw 45 ma which means close to useless for running off batteries, unless you use a car battery.