Ski selecting

I'd look to buy boots before skis, purely on the basis of comfort really! If you're comfy you're more likely to ski better as well I'd say. Plus you've then got a constant and if you try a few different skis then you'll notice any difference. Also, don't be tempted to think more expensive / higher level boots will make you a better skier, it might be the opposite. A good ski shop should help you out.

Boots first, well fitted boots have such a positive effect on the whole skiing experience.
In terms of ski, unless you really know your stuff, be guided by the shop. I generally hire from the “premium” range and let the shop tell me what will suit the way I ski, if they don’t work after a day or 2 I go back and change them.

As others have said, if you go enough, seriously consider getting some well fitted boots to save time, improve comfort and increase enjoyment. I assume you are still renting and curious on the selection though.

It's hard to say how much difference you will feel - when you know, you know but without knowing how many days you do, your ability and aspirations and style then you need to try it out.

Most resort hire shops are pretty open to a swap during the week. Have a word when you hire and ask them if there are options, then maybe pop back and swap depending on how you feel and what the conditions are. Try different lengths and see - rough rule of thumb is very much like bikes - longer are more stable, harder to turn but faster and floats better off piste, shorter are easier to turn but less stable. Stiffer hold edges better but need more power and technique.

As above, boots are worth investing in, the rent skis and don’t be afraid to swap them if not convinced

It's years since I skied but I always reckoned go much softer than you think you need in both boots and skis or you'll end up fighting the gear and not enjoying yourself much. I was skiing with a guide once who also made a big thing about how light his bindings were set - "if you ski properly you don't need to tighten your bindings right down". As if to demonstrate he shook his foot and his ski fell off the chairlift. Oh how we laughed.

Stiffer hold edges better but need more power and technique.

Though don't confuse longitudinal stiffness with torsional stiffness. Skis can have soft tips and tails whilst also having good edge grip.

Any rental shop I've ever used has asked your weight, ability and check your height, so you should be getting looked after in that respect.

Stiffer = more stability at speed I think.
Thinner = less stability at speed, but easier to put turns in with.

At resort shops I've always got a reasonable ski, sometimes a little heavy and inflexible, the only major difference was renting in Chamonix once when we ended up with the lightest most flexible ski I've ever had, was hard to stop and stay still on them as they moved so well. I tend to think ski profile makes a difference to good skiers, I'm a bit below average so it's less relevant to me.

Interesting thoughts above. I haven’t skied in about 10 years, but was obsessed as a late teen.

I once made a slight error in a rental shop, as after trying on boots I slipped my feet back into trainers, standing on tip toes so as not to squash the backs of my Nikes. The ski tech then sized up my height, asked about capability etc and I left with a pair of longer, stiffer skis than I had ever used before. They were brilliant on and off piste all week- took me a few days to work out why!!

How much difference would I feel between a stronger or more flexible ski?

See, I reckon most skiers would agree almost all skis have their place, stronger or more bendy (technical terms, I beleive 😉 ). It depends what you are up to, snow conditions and a range of other factors.

As you mention hiring, it would seem sensible to go with a place that allows you to chop and change. I'll mention Skimium rental shops here - which as far as I can tell is the rental arm of Decathlon. They will let you change between skis on the 'level' you have paid for. Make yourself try some different skis and see what works for you, piste skis, freeride skis, freestyle skis - anything you can, suitable to the conditions. You will definitely notice difference, but I'm not sure there is a silver bullet, much like bikes - and the diversity is a good thing.

These days for the vast majority of skiers a decent all mountain ski will cover everything. Unless you’re heavy and stick to groomed runs at speed pretty much all the time I don’t think you want something too stiff. Long tips and tails are the norm these days meaning that overall an all mountain ski will be a bit longer than they were a few years ago, although the carving edge hasn’t changed much. The longer tips and tails are lovely in softer snow. I prefer a light ski for moguls and adventuring off piste.
If you’re interested you can get into turning radius and the like but for most this won’t matter too much. Many production skis have pretty poor construction and thin edges though so for skis that I own myself I prefer the handmade boutique brands - you pay more but my last pair from Icelantic lasted me more than 10 years with some basic home maintenance inbetween each use. Even when I finally retired them it was because of binding failure, the bases were still fine and edges despite many years of being resharpened were still really good.

May be all except our OP and me are in the "normal" weight range and haven't been on skis that don't suit.

Alchiltern is exactly the same weight as me skiing with Madame sitting on my shoulders. Without Madame on my shoulders I'll have 15 % less weight/cm2 of ski if I'm on 165/64 slalom skis and he's on 185/120 freeride skis.

I often use women's skis, the last men's skis I bought were Dynastar Mythic - far too stiff for me, I couldn't carve them, they're in the cupboard devoid of bindings. Even junior who is powerful but not especially heavy used women's GS skis for skicross.

So if I were you rather than 65kg me I'd be looking at very stiff piste skis and wide stiff skis off-piste, Al.