Welcome to the Bunnings Workshop community. It's wonderful to have you join us, and thank you for sharing your question about how to paint or varnish your doorstep.
This is the perfect opportunity for a revamp of your doorstep. If you wish to paint it in the same colour, I suggest using Cabot's 4L Brown Timbercolour Deck And Exterior Paint. It's rated for exterior use and is self-priming, saving you from having to purchase a separate paint primer. Because it is intended for deck use, it's been formulated to be stepped on and will withstand rough use.
The rules for applying either paint or water-based decking oil are the same. The doorstep must be sanded down first to remove all the old paint that's been put on the timber piece. I suggest using an Ozito 200W Detail Sander, it has multiple pads already included which will be more than enough to remove the paint that's presently on there. Wipe the timber with a damp cloth to remove all the timber dust. My number one suggestion is to test a small corner of the doorstep with the paint or oil that you've chosen to make sure that you're happy with the results.
If you need further assistance, please let us know.