Radioactive materials are used in a variety of medical applications for diagnostic, therapeutic and research purposes and a wide range of radioactive waste is produced. The most important characteristics of biomedical waste are its short half-life and low radiotoxicity. Biomedical waste typically contains low energy beta and gamma emitters and is generally of low total and specific activity. The most commonly used instruments to detect of beta radiation is a liquid scintillation spectrometer. For detection of gamma photons with very low energy it is necessary to use a special semiconductor detector. See refferences: https://www.epa.gov/sites/production/files/2015-05/documents/appendixD.pdf
The simplest and easiest way it to use a gm counter that can give you fairly good information without having the direct contact with the waste materials. This is also simplest way of radiation monitoring.Most of the radiation monitors are based on gm counting system.Any calibrated monitor will give you accurate measure of absolute concentration.
For identification of waste contaminating isotopes the sample may be taken to semi conductor detectors after ascertaining that the radiation dose level is well within the handling dose.
The first step is to separate the radioactive materials for precise measurements. If some short-lived radionuclides are expected, the half-lives must be considered during separation. For the estimation of amount, gamma spectroscopy is a better choice for gamma emitters and scintillation counter for charged particle emitters.:
I think its depends on the state of the waste , solid or liquid . beside you must have some information about the radionuclides may exist in the original ampules to build up your search about it in the studied samples.
What are the criteria for storage or disposal? You can use a gm counter at a distance of (say) one meter to measure total activity (curies, say) or in close contact to measure the activity in particular items. What is the purpose of the measurement? Is it a disposal criterion?
Depending ion the type of waste, solid? Liquid? Vials?
And again whta kind of emission? Gamma+Beta or Gamma+Alpha? Or are present a rafdionuclides mix...
I think the best way is: 1) Idetify the radionuclides, so you can know the emission type, the activity, 2) Phisycal status, solid or liquid, or mix (vials for example) 3) How is the storge of medical waste, drums, barrel, big containment tub... Now you could know what is the best method to measure the radioactivity in medical waste.
My personal opinion is:
LSC, liquid scintillation counting, to measure medical liquid waste. Is the best method to identify Beta, but alpha too, emitters.
Gamma spectrometry to measure medical solid waste and/or liquid waste.
These the methods to know the activity and know what nuclides are present in the waste if thay are not known with high precision.
In the case you want know the dose rate, to understand the worker and people exposition, the best solutions are portable instruments to measure H*(10), Environmental Equivalent Dose.