Can you develop an independent, secure oracle for your dApp?

Random numbers and blockchains don't go together very well due to the fact a blockchain is deterministic. This means you should not rely on any on-chain values for a source of randomness (like block hashes or timestamps etc), as they can be manipulated or pre-determined by miners and used to game your contract that relies on randomness.

In addition to this, just using an oracle to get a source of randomness from an external API is also strongly discouraged, because there's no real way of knowing if the returned number is actually random, of it's been sent back by a malicious actor wanting to game your contract that relies on it. Ie if your oracle returned 123456789, how do you know if its a truly random number, or if its returning that because it knows it can then call your contract and take funds if that random number is used?

This is where a verifiable random number comes into play. With a verifiable random number, an oracle is used, however there is a seed generated based on something (could be user input or on-chain data, it doesn't matter) before the call to the oracle is made (the call passes the seed to the oracle). Once the oracle generates a random number, the VRF function can then use math and cryptography to actually verify that the random number was created based from the initial seed, and that it's not just some random number plucked from the air (and potentially malicious). This is the magic of VRF, being able to verify a random number was created with a previously committed seed. So combining a VRF function with an oracle is the best possible way for a safe and secure source of randomness in a smart contract.

Chainlink VRF is the industry standard for randomness on blockchains, and I highly suggest you look into it. If it's cost you're worried about, I think its cheaper to use on other chains like Polygon or BSC. Also if you speak to the Chainlink Labs team, they can possibly work out some agreement that is more feasible for bootstrapped projects