I agree that following them and seeing what they're curious about is probably the easiest. At this point I wouldn't anticipate too much beyond a few outlet covers, blind cord wrappers and a few cabinet locks (preferably the over-the-handle ones, and not the ones that need screws). If you know you have tippy furniture, a furniture strap isn't a bad idea, but even in earthquake country we haven't secured anything to the walls because DS just isn't a climber. And the blind cord things DS has figured out how to defeat pretty easily (in the Living Room) - although by that time it was less of a concern. We had cordless blinds installed in his bedroom so it wouldn't be a concern there.
Doorknob covers were a total waste for us - DS didn't figure out doorknobs AND develop the hand strength to turn them until after 2yo. He only last week managed to open the front door - and he hasn't figured out the lock yet. He could reach light switches and the kitchen counter before 2, but that's really unusual.
We never bothered with a toilet lock, or securing any of the kitchen cabinets except the one under the sink. We moved all medicine to the top shelf (in the back) of the standing medicine chest, or to the over-the-sink one. I'm not concerned about him getting into the medicine chest and playing with the bandaids or the lotion or the washcloths (the stuff he can reach).
What we did wind up getting is gates. We have 3 gates that come with the pre-cut pet door. They weren't easy to find, but it's made life a LOT easier for our geriatric cat. She can escape DS when she wants, but isn't locked into a room (since she can't jump them). We did have to get a different gate for one door, since our doors are not standard size (we're in an old Victorian), we have a few doors that are too narrow for standard gates. So if you're in an older house, be sure to measure your door frames before getting gates. For top of stairs, you will need a mounted gate - a pressure gate is not safe there. I can knock over a pressure gate with little work, and DS has discovered it doesn't take a lot of tugging to get some of them down. Do spend a little on your gates though, the cheap ones are exactly that - cheap. We had 2 of them splinter on us after less than 6 months use - the wood just wasn't up to that kind of pressure.
And for kitchen safety, when they can reach the counter, the 12 inch rule goes into effect (keeping anything dangerous 12 inches back from the edge). We spent a few months with no knobs on the stove, since I didn't want him blowing us up (we have a gas stove), but that phase passed quickly. And now I just have to be sure to turn the handles in so he can't grab them.
Obviously, if your kid is pulling drawers out on their head, flushing things, climbing furniture, etc., you're going to need to take steps, but most of those kinds of things are available locally (our local hardware store has all sorts of childproofing stuff), and don't cost a whole lot.