Which one should I go for, or are they all much of a muchness?
There's Mounjaro and Wegovy. Its up to you which you choose. However, Mounjaro targets two hormones instead of one (Wegovy) and has been licensed for treating obesity in the UK. Also known in the trials to cause higher percentage of weightloss than Wegovy. However both of them work for people. If you don't have a bmi of 30 and above, or a bmi of 27 and above with other qualifying health conditions or from other ethnicities, you will not qualify for WLI as you'd not be classed as obese.
Can you just do it for a month or is there a longer commitment involved?
Technically, you can do it for a month if you choose. Even the subcription-based ones would still let you cancel anytime easily so you're not stuck with them. However, the chances of you meeting your goal for a month is unknown. It would be better to expect less results than more so as not to be disappointed when you don't meet a high expectation. It's not a quick fix and you may not lose what you expect to lose in a month.
What is likely to happen in a month? Is it worth it?
No one knows. This prescription medication is not a quick fix for weightloss. You can't go on it and give it one month to lose 1 stone because it may or may not happen to you. 1 month on it is only the very beginning and the least you can do. If you lose a stone, great, lucky for you but don't expect to do so, again to avoid disappointment.
You'll have to see how your body responds to it first as it differs from person to person, and it also works randomly (eg; loss this week and no loss next week; side effect today and nothing tomorrow or continuous loss or no loss at all or constant side effects or no side effects at all, etc). You just can't tell, therefore the benefits will have to outweigh the risks to you, and you need to be patient on it as well as balancing being on a calorie deficit with eating properly. That is if you qualify for the medication to start with.
To start, you'll need to go through the consultation online with the registered pharmacy you choose and answer all the questions honestly so that if you qualify, you will be approved and you can begin your journey, but if you have issues that would cause you to be declined (like a disqualifying health condition or medication, lower bmi, etc), then you'll know and find alternatives.