There are plenty of options open to you.
Less than $100, as long as you're not including the cost of the balloon and the gas, there are still so many options.
The most obvious is Ham Radio. There's heaps of bands to choose from and no shortage of radios either off the shelf, modified or home made.
APRS makes tracking the balloon and recovering the data and the equipment easy. There are plenty of examples.
http://projecthorus.org/
One thing you can count on is some people will underestimate the capabilities of some circuits.
The first choice is LIPD's. These little transmitters are so easily dismissed but when put to a disposable task they always out perform expectations.
I was asked to construct a simple balloon payload, it was to ride on a party balloon and I was given 30 minutes to construct it.
I used a $5 434MHz 50mW LIPD, a 555 timer and a thermistor running on a tiny 3V lithium recovered from a tiny IR helicopter from a bargain bin for $2.
I calibrated the circuit with freeze spray and measured the response. Total cost less than $10 less the cost of the balloon. Total weight, 12 grams.
Education and fun - priceless
The circuit was picked up and I never saw it again. I did not intend to recover it, but recorded the pulses from the LIPD.
The balloon was launched 20km from my home behind a hill. I did not hear the payload until about 2 minutes after launch.
I then listened to the signal for about an hour until the balloon popped and I could hear its rapid decent through three inversion layers and the signal was lost.
From the estimate temperature compared to weather balloon data for the day from the local airport, it flew to about 20,000ft when it popped.
Now this isn't edge of space, that's still another 100,000ft. But the signal from the LIPD was still easily heard well over 25km as the balloon drifted away from my location. So it's certainly capable of high altitudes not considering other factors like temperature.
In Australia we have the option of using UHF CB ~477MHz. In the USA, FRS and GPRS perform much the same role. A cheap 500mW transceiver can be sourced for less than $20. So while it's heavier than a LIPD, it is barely double the price. When stripped of it's plastic case, only the batteries to power it are a weight concern.
For everybody else, 27MHz is another good option. It's not hard to find some simple 5W 27MHz AM boards which are only a also quite light. The only issue is powering them. Though lithium batteries can easily manage the task if the transmitter duty cycle is controlled.
Currently my local club has two balloon projects on the bench. A large payload balloon which is carrying television transmitters, radiation monitors, APRS and a swag of other little experiments including releasing paper aeroplanes.
The other is a bare bones payload. Because of the amazing success of the LIPD flight and other lipd tests, this project was thought up. The goal is to keep everything as cheap as possible, small as possible and recoverable.
This means a party balloon (though a heavy duty one). SMD APRS for tracking using a GPS chip and radiometrix transmitter. This time instead of using a recycled lithium battery, a new lithium will be used. The total cost so far is less than $60 for everything except for the balloon and gas and the payload is just a little bigger than a postage stamp. It is expected that this balloon should make it to 30,000ft. If we can get away with under inflating the balloon, then it may be higher.