I was always taught to let the engine do the braking.
Approaching red lights, foot off the gas & the vehicle slows. As the speed drops, drop into 3rd - the revs should be just above normal to give you that extra bit of control should you need to accellerate.
With practice I often get to the lights without touching my brakes, still rolling along in 2nd & good to go as the lights change without having to worry about the most appropriate gear to be in.
At my last assessment, the young bloke insisted I was doing it all wrong & that I should stay in 4th right up to the lights & use the brakes to slow me, pressing the clutch just before the engine stalls - which was fine until he realised that the bus couldn't do 20mph in 4th without stalling!
So, my choice was, clutch & cruise (so, not in control of the vehicle) or drop down the gears which his manual doesn't recommend.
Same with going down hills. I've seen the end result of too many sitting on their brakes then finding out they have lost them & running out of road. Earlier this year I was in the lakes, going over wrynose (sp) pass, on the downhills I rarely touched the brakes, just dropped into 2nd and let the engine do the braking. It was quite happy to go down those hills at a steady, controllable speed without racing away.
Back to the assessment, the assessor also tried to persuade me to use block gear change - Hmmm
Pull out of a junction, across a road (for example) in 1st, you HAVE to hit 2nd before you get to the white lines in the middle. Go from 1st straight to 3rd and it stalls - it simply cannot move the weight, even trying 2nd to 4th doesn't work - it has no 'poke' and the engine simply 'pinks' and struggles.
The ONLY block changes I can do are 3rd to 5th or 4th to 6th
Sounds like your assessor needing assessing! 1st to 3rd when setting off, in a bus?