Brake only touches rim occasionally when brake applied

If you have to pull hard on the brake lever to get the pads to full engage on the rim, the brake caliper is not adjusted properly. Rim brakes can only generate stopping force when both pads are applying opposing 'gripping' forces to the rim.

New bike should be set up correctly, if you bought from a dedicated bicycle store take it back and and ask for the brake calipers to be adjusted. If you bought from a 'big box' store or general sports store the staff probably do not have expertise to do this properly, so you should seek out a bicycle repair shop to help you.

If you want to address this yourself, there is plenty of guidance on-line. Park Tool Repair Help is particularly good.

It also seems from you description that your wheels may be out of true. This can prevent the pads from being adjusted closely enough to the rim. First check the wheel is properly seated in the fork or frame drop-out slots before the quick-release or axle nuts are tightened. You can visually check the trueness of the rim by spinning the wheel slowly and observing the distance between the rim and a brake pad. If the distance varies by more than a couple of millimeters the wheel may need truing. This is not a trivial process so enlist the help of a bike repair shop