OK so with her stats, if she continues on the same lines she'd be able to stay in the Besafe Stretch up to about 8 years old if you so wanted. It costs about £450 - so higher than your budget. There are cheaper seats of a similar style such as Axkid Move. That would probably last her to about age 7. It costs £250 and is just as safe as the Besafe, but has a few less features - the Besafe can be reclined on the go whereas Axkid Move you pick the recline and stick with it, usually by age. It's easier to change the height of the straps in the Besafe whereas Axkid Move is more of a faff, but you only need to do it twice ever. These are examples of the longest lasting rear facing seats on the market (25kg+ ERF seats). With her weight/height it's probably not worth the extra £200 just to get another year out of it, whereas for a child who is very high on the scales, that might be worth paying.
Of course you don't have to keep using it that long anyway - it would just essentially mean that you have complete freedom to move her into a high backed booster whenever you feel the time is right without worrying about her weight or height. And another point (which could be positive or negative depending on your perspective) is that you don't have the option to forward face. Rear facing is the safest option, so some people like the fact of being locked into that in order to avoid any arguments with partner/relatives/pester power/general temptation. But as they get older, especially after 4 years, it isn't (statistically) as important and some people prefer to know that they have the option to change to forward facing if they want to.
In contrast an 18kg seat like most of the spin ones, she'll likely outgrow just about round 4 years old. Attitudes are changing about booster seats - people used to say fine as long as over age 3.5, age 4 is better - but more and more people are choosing to keep a 5 point harness until more like 4/5 years, and I'd guess this trend will continue for the next 3 years or so. So you'd be potentially looking at changing a bit early if you went for a standard spin seat. However, this isn't necessarily the end of the world, because there are now quite a few seats on the market that combine harness (forward facing) and booster seat up to about 105cm / 20kg, or 125cm / 25kg, and these would be a good transition seat for her if she outgrows it, but you still feel she's a bit young for seatbelt only. So you could get a standard spin (e.g. Joie 360 Spin) until she's about 3.5, and then later one of the harness/booster seats so she can harness until about 4.5 - 5yo and then change to booster. This might also be a good solution if you think you'll have another child and pass the seat down.
Or there is the new Britax Dualfix M Plus, that's rear facing/forward facing, spin up to 105cm and 20kg - which will take her to about age 4.5 which is a bit better than the standard 18kg. This costs about £325 so it's cheaper than the Besafe, but more expensive than the Axkid Move. Lovely seat to use, nice harness, nice adjustment, great safety reputation from Britax, only the 105cm limit will be a problem for some taller children. I actually really like this seat, and given your updated requirements it would be my vote, but look into different options, see if you can try them out with your DD and in your car. It's you that will use it so it's helpful to get a feel for different models.
The ones that go all the way up to 12 will mostly be a bit of a gamble for you, because she's on the borderline on the weight category so you might have the same 18kg issue. Also, they tend to be bulkier, they perform a bit worse for safety in all modes and they are not usually cheaper than buying a separate spin seat + high backed booster, but if you did want to look at one then I'd look at Silver Cross All Motion 360, as that recently got a surprisingly good score in the crash testing, better than most all-stages seats, (although still worse than the best spin seats, best high back boosters and the seats like Besafe/Axkid) and like the Britax, it has a slightly higher weight limit for the rear facing or 5 point harness stage, although it's only 18.5kg, not as high as 20kg, but that might be enough to get you to about 4.5 years. It costs about £400, so it's right at your budget whereas a standard spin seat is about £160-280, and the Britax with the higher limit is £325. A top range high backed booster is currently about £150-180 and a medium one about £100. So it's not much of a saving, and if you have a second child then you won't be able to hand it down if your DD is still using it.
Weight wise, it is common for them to drop a centile when they start to move, so if she's not started walking properly yet, it could be she'd get a little bit longer in some of the lower weight limit seats. All of the ages/weights are just guesswork I'm afraid but gives you a rough idea.
Anyway yes - most important thing actually is to try seats out and see how you get on with them. Have a look at her fit, the ease of using different features and how it fits in your car ideally before you buy. I know it's tempting to buy online but this is a really useful and valuable step, especially if you can find a retailer that you can go back to for advice if you ever have any issues with the seat.