C.P.
I really like my wall-mounted gates... can't remember the brand or model, but they were about $25 at Babies R' Us. I think it would be difficult for a little kid to open (and especially close) ANY pressure-mounted gate. You could always just fill in the holes with putty and re-paint when you get ready to move (if you install wall-mounted gates).
You could also re-think the location of gates. For example, can your 3-year-old open the bathroom door? If so, you might just plan to use the door rather than putting up another gate. What I did when my girl started getting mobile was go through and "baby-proof" as much as I could. All nick-nacks off of lower tables, block all outlets and power cords, get in the habit of NOT putting drinks/food within reach, etc. Start teaching her what she can not touch, keep toys around the house as easy distractors (when she does start getting into things she's not supposed to).
In my house, the gates were to keep her out of the kitchen (danger & dirty) and to block off the hallway (bedrooms & bathroom--where we kept litter box, cleaning stuff, etc). Now that she is 15 months old, I only use the kitchen gate when I am cooking and don't want her underfoot (she knows not to go in the cabinets or trash). And, the hallway gate is used on weekend mornings to keep her IN the bedroom area (so I can sleep in). We just keep the bathroom door closed and the cat's stuff (litter box & food) is kept blocked off in a corner so she can't get to them.
Good luck!