Regarding your 10g with the bacteria bloom. What are the ammonia and nitrite readings? Three weeks into a fish-in cycle is a critical time for the cycle and for the fish.
Many of us use sponge filters. They use an airpump to make bubbles to pull the water through the sponge (media). Tetra makes a good reliable cheap pump. These are top-of-the-line filters: Aquarium Sponge Filter; ATI Bio Filters and Replacement Hydro Sponges.
Cheaper ones are available on Amazon.
Matt's right, cycling with shrimp is a smelly mess and can breed mold. Fishfood is marginally better. Pure ammonia (that does NOT foam when shaken) is best. Ammonia is to feed the bacteria.
Placing an uncycled filter in a cycled tank for a couple of weeks will "seed" that filter with bacteria. Putting a cycled filter into a new tank effectively cycles that tank.
Will you be running two tanks (the 10g and the 25g)? Wait until the 10g is fully established (cycled) and seed your 25g filter by installing it in that tank. Whenever you remove or replace a filter, monitor your parameters closely to guard against mini-cycles (ammonia spikes).
You're a gardener. Great! For water safety (and a calm sorority), use as many live plants as you can manage, especially floaters.