OP_RETURN
The generally approved way to include arbitrary content in a transaction is by use of an OP_RETURN script. See Explanation of what an OP_RETURN transaction looks like
There is nothing you can write in a Bitcoin script that checks the number of other transactions in a block. The only way to ensure exclusivity is to make the transaction sufficiently large.
Transaction size
To be sure your transaction is the only non-coinbase transaction in a block it would have to be large enough to almost fill the block. See What is the maximum size of a transaction?
Personally, I don't see how the presence of other transactions could in any way affect the perceived importance of a transaction, but I'll disregard that aspect.
Payment Conditions
To be sure that you only pay the miner after the transaction is included in a valid block, you only have to use one output of your transaction to pay the miner a large transaction fee. For example with inputs of 1.0001 BTC and an output to yourself of 0.0001 BTC. leaving 1.0000 BTC to be collected by the miner.
Minimum relay fee
Large transactions will not be relayed by many intermediary nodes unless the mining fee exceeds a minimum amount. I believe initially this was 1000 satoshis per vkByte. This could mean that you either need to pay more than 1 BTC or need to make a special arrangement with a miner to deliver your unconfirmed transaction to them using some direct method.
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