BTW not sure how it works in your area, but in here a lot of plants are given away by other aquarist when they are doing tank maintenance. It is all the fast growing plants that are needed in the beginning of the setup, frogbit, duckweed, hornwort, lot of mosses and so. Join some facebook groups and look for people giving these away or even ask for some. Lot of plants like java fern are also regularly cut, a lot of people have anubias cuttings too. If I were closer I could give you bucket (and I have often done so and I also received a lot of plants that I needed in the beginning), basically except one echinodorus, I have never purchased plants for my current three tanks in the past 3 years.
There are also people selling stuff due to move or upgrades, so marketplace or specific website exchanges for lights and used heaters or filters are not a bad option.
For a 29 gallon a large sponge and a simple airfilter are more than enough (provided you will do water changes regularly or get the fast growing plants), and the air filter itself costs like 16 euro tops, and you cab buy the sponge sold regularly, or check for shops that will cut the sponges with higher PPI (or what is it called, the how small a hole in the netting is) and you can buy a large cut sponge for lwe price than the commercial sold and packed one. I bought a 20x10x20cm sponge for 4 euros and it has the large space the bacteria needs. It doesnt look pretty though, so there is that, but it can be hidden by a large plant (example of not looking so pretty below from my tank)
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You can do a lot of things on a budget, you dont need to do everything at once and you can easily do a fishless cycle, add some plants in the upcoming weeks as you get them, wait some more weeks, move the platy you have, as it is a hardy fish, still wait, give the plants some more time, move some other fish and do this in a span of months rather than a weekend