It's funny because I never have this problem! LOL!

Basically you just want to identify a strong upright limb and remove the lower side limbs, I would think.

Pruning will only encourage branching if you leave at least 8 inches or more of a stump. If you trim a branch closer to the trunk, you should not get any sprouting from what's left.

However, all varieties are slightly different. 'Penang Peach' is more compact. 'Divine' tends to grow bushy and lower. 'Cookstown Sunset' or 'Miami Rose' tend to be very vigorous and grow very grow tall.

There are PLENTY of very tall varieties that should make good trees for you. Maybe you should switch varieties?

Which one do you have?

Here's a pic of the front view.

Another pic of the side. You can see where I pruned last year, and new branches (unwanted) were formed.
I don't want it to branch until it gets taller first.
Advice on where to prune would be appreciated. Thanks.

Oh, also I should mention that I do not wish to prune the newer growth on top, just the bottom branches. I am actually afraid to prune it because I don't want it to go crazy and make even more branches. One of my neighbors has a plumeria that they kept pruning, and it just kept getting wider and wider until it was about 10 feet across!

It doesn't seem to matter how much stump you leave, the
plant will grow from there. It's best to completely remove
limbs as close as possible to the trunk.

One year I pruned and one that I thought I had cut close
enough wasn't. The top of the limb was fine, but the bottom
had about a half-inch of limb left. It formed two new
branches from there.

Pick the staightest up, trunk-like limb for your main
trunk. The rest could go. I'd make it a multi-year
project and not remove all the side branches right away.

After you've pruned and if side branches pop up, just cut
them off while they're young. This would be your best
long-term procedure.