You want to ensure that the starter will not engage with the engine running, as this will damage the starter. It needs to disengage immediately once the engine kicks on, and that could be tricky.
You ideally want a fairly secure link. The car starting itself while in a closed garage could be dangerous!
Also, you're basically going to have a relay that jumps the RUN wire, bypassing the requirement to have a key in the car entirely. There's some safety issues there if you couldn't turn off the car! I'm not sure how this works, I've never had keyless ignition. I think you'd want to keep the car running for a maximum of say 5 or 10 min and disengage the RUN relay in favor of the key once the key's been inserted and turned to RUN, but I'm not sure how you'd detect that since the RUN line is already energized by the RUN-relay.
If it's a standard, you need to ensure it's not in gear before hitting the starter. Sometimes you put a standard in gear while parked to keep it from rolling on an incline as a backup to the parking brake.
A carb'ed engine may need the accelerator pumped to set the choke prior to starting. You couldn't do this on such a vehicle. You'd want a fuel-injected one.
Many newer cars use "smart keys" that make it difficult to wire around the starter. What you're doing is exactly the same as hotwiring a car, start it without a key by connecting wires together! The security features to prevent that may make it impractical to install a remote starter.