Changing your outlets to make the first three always hot while keeping the last one as a switched outlet can be done, but it involves some electrical work that should be approached with caution.
You are correct that you would need to connect the wires correctly. To achieve this, you would typically do the following:
1. Turn off the power at the circuit breaker to ensure safety.
2. Remove the outlet covers and unscrew the outlets from the boxes.
3. Identify the wires connected to the switched outlet and the hot wires.
4. For the first three outlets, you can connect the hot wire from the top terminal of the first outlet to the bottom terminal (load) of the same outlet, effectively making it always hot.
5. You would then need to run a jumper wire from the first outlet's bottom terminal to the second outlet's bottom terminal, and repeat for the third outlet.
6. Ensure the last outlet retains its connection to the switch.
Since this involves working with electrical wiring, I recommend hiring a licensed electrician to ensure everything is done safely and up to code. Typical costs for this type of work can range from $150 to $300, depending on your location and the complexity of the job.
As a next step, consider getting 2-3 local quotes on Handyman.com to find a qualified electrician for this project.
— Assisted answer