puncture/pump advice

CO2 Inflator and a pump with a hose as backup (Lezeyne or Topeak Race Rocket are pretty good - check the max psi). Top tip though; sacrifice a CO2 canister and have a practice at home. I was on a great 60 mile solo route round the Tarn in France and punctured. CO2 Inflator failed and I had to phone my wife for a rescue. Gutted that I'd not completed the route and didn't have a backup pump. LBS replaced it and checked the new one worked; as well as giving me some free CO2 cannisters.

they've gone out of fashion but a full size 'long' pump is still the best for quick and relatively effortless inflation. I have an old plastic Zefal HP that fits in the commuter rucksack and has unfortunately seen more use than I'd like in the last few weeks. Can't beat them though I have a Lezyne pressure drive which is about as good as a micro pump gets.

I've had 1 puncture in the 2 years since I started cycling (tempting fate!) and had no problem getting up to pressure using my Lezyne Road Drive.

I've got a Topeak Road Morph for my tourer, that lives in the pannier and comes highly recommended. For my road bikes, I prefere the Topeak Race Rocket HPX. Both have flexible hoses, the Road Morph is quicker, being a mini track pump, but is also considerably bigger/heavier. For smaller/lighter, the HPX is very good, but takes longer to get 100 psi. I guess you pays your money and takes your choice.

I have CO2 and a pump, the CO2 is to get me going again, and the pump as Back-up

I've got a couple of Birzman pumps (one's a Horizons and the other is the newer version with the snap-it head) and can recommend them. They're really nicely made and properly capable of sticking 100psi in your tyres, but still small enough for a jersey pocket.

I have used CO2 for m/c puntures for 30 years. Great things. Of course they only work once.
I often carry the pump but also 1 CO2 bulb. That will get 100psi+ in and there is still a pump as a back up.
Having aid that I have never had to hold the pump onto the valve and I have the same pump as you. Any pump where you don't have a hose has to be held with your finger supporting the valve so those finger almost automatically hold the pump as well. In fact that allows a two handed action which is great at high pressure. 1 other thing. The longer the pump, the better it will be.

+1 for the Topeak Road Morph. When you are using it you have one hand free to hold the bike steady. I've used mine several times and always found pumping the least frustrating part of the whole procedure

A hose on the pump is an essential as far as I am concerned.

I have a Topeak Road Morph attached to the skinny bike and a Lezyne job (which maxes out at 95psi) in the pannier for the bigger tyres on the commuter.

Both are excellent. I did however end up wrapping bar tape round the Lezyne as it was too slippy.