Basically what you want to test is bacterial presence. Without some microbiology experience you will struggle to ID most bacteria, but there are some things you can do at home that might give you some help.
With stuff you (might) have at home:
Make some home-made bacterial culture plates: Make a stock with about 0.5% salt (5 g/litre), add some milk powder (or, even better, protein shake) to about 20 g/litre, dissolve. Add gelatine to about 15 g/litre (1.5%). Boil gently until gelatine is dissolved. Even better, do this in a pressure cooker to ensure sterility.
Pour while hot into clean, shallow, preferably clear, vessels (If you want them sterile, heat in oven to 180 C/375 F for 10 min) and allow to cool until set while covered with a plate or dish or clingfilm (leave a small gap to allow steam to escape -you don't want a lot of condensation) . These are your bacterial plates. They are fairly rudimentary in terms of science, but should give you a start.
Take a small sample of your meats; a gram or so should do it. Soak in a small amount (maybe 2-5 ml/teaspoon) of boiled cooled water in a closed clean container to re-hydrate (time??, until soft) and then mush up to the best of your ability in the water with a clean (preferably sterilized) implement.
Wearing clean gloves, take a clean cottonbud/Q-tip out of a new, freshly opened package (i.e. don't use your old ones that have been sitting on your counter for ages). Make sure you don't touch one end as you get it out of the package. Dip the clean end into the meat mush water and carefully wipe over the entire surface of your "plates". I usually do this in a close zig-zag fashion across the plate, rotate plate about 1/3, repeat zig-zag, rotate 1/3 and repeat again. Cover the plates with clingfilm. Repeat this process with only your water (this is your control to test your sterile technique)
Incubate the plates in a warm location - ideally between 25 C (77 F) and 37 C (98.6 F) overnight.
The next morning, observe what's on your plates - if there's nothing, you have no concerns at all. Look for small circles, often pale tan or whitish or grey; these are colonies of microorganisms. A few colonies (say 10-20) may be probably OK (though would depend on species), but lots, or an entirely covered plate means you have some problems or you didn't do it correctly. Check your control plate - it should have nothing growing. If it is growing things, then you have some sterility issues in your processes and you should compare this plate to your sample plate. Look at any colony shapes and colours and if they have done anything to the plate colour or texture. Bright yellow/orange colonies are probably yeasts, anything else has a good chance of being a bacterium.
To do anything further you need a microscope and some stains. It gets a bit technical, so I won't go into it here, but look up home-made bacterial stains - you can use some food dyes or gentian/crystal violet.