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I'd like to create a contract through which people can set publicly available key=value information in exchange for some Ether sent to me (the owner of the contract).
This is to create a public decentralized database on which anyone can read and write, and the Ether cost would be to limit spam.

However, I'd like it to be free for all users to retrieve any key stored in the contract. My understanding of Ethereum is limited, is this possible?

I'd like to create a contract through which people can set publicly
available key=value information

You can use a mapping to store data and public method to set values

exchange for some Ether sent to me (the owner of the contract)

You can make the set method payable and check for an amount of Ether from sender

I'd like it to be free for all users to retrieve any key stored in the
contract

You can create the function a view one so no cost or transaction invlolved in reading values

is this possible?

Yes, This looks possible. It would look like below.

pragma solidity >=0.4.22 <0.6.0;

contract Store 
 mapping(bytes32 => bytes32) public keyValStore;
 address payable public owner; 
 uint storeFee;

 constructor(uint fee) public 
 owner = msg.sender; // setting contract creator address as the owner
 storeFee = fee; // setting a store fee for to set values
 

 function set(bytes32 key, bytes32 value) public payable 
 require(msg.value >= storeFee); // check if Ether value is greater than the store fee
 owner.transfer(msg.value); // transfer Ether to owner account
 keyValStore[key] = value; // setting the key value pair in mapping
 

 function get(bytes32 key) public view returns (bytes32) 
 bytes32 val = keyValStore[key]; // get the relavant value for the given key
 return val;
 

Yes it's possible, here's an example key/value store contract to help you get started that requires 1 ether to set a key/value and anyone can read the data for free:

pragma solidity >=0.4.22 <0.6.0;
contract Store 
 mapping(bytes32 => bytes32) private store;
 mapping(bytes32 => address) private authors;
 address private owner;

 constructor() public 
 owner = msg.sender;
 

 function set(bytes32 key, bytes32 value) public payable 

 function get(bytes32 key) public view returns(bytes32) 
 return store[key];
 

 function withdraw(address payable receiver) public 
 require(msg.sender == owner);
 receiver.transfer(address(this).balance);
 

https://rinkeby.etherscan.io/address/0xf7e0caef5cd7a18d31343670b60ff463fa23d5c8