Yes it does impact what car seat is best.
So on those centiles she is likely to outgrow the "up to 4 years" seats towards the later half of being three. That's too young to move into a booster seat, so you will likely need to buy another harnessed seat at that age if you go for that option. These are more expensive than high backed booster seats, and the ones which combine a 5-point-harness stage with a booster stage tend to have a less reliable safety rating, although honestly, they are improving.
However, if you plan to have another child this can be a reasonable solution - keep the new baby in the spinning seat and move older sibling to a harness + booster combo seat, or a larger rear facing seat.
But if you are likely to only have one child and want to stay rear facing at that age (which is the safest option) it can be frustrating if you realise that you need to buy a larger rear facing seat when you could have simply started with one in the first place.
So to start with the larger rear facing seats which are suitable from birth up to 125cm, you've basically got four choices:
Avionaut Sky
Besafe Stretch B
Axkid One2 +
Joie i-Prodigi
The Axkid is probably the bees knees of these - it's isofix fitted, light to move between cars and has a great newborn insert. However it does have a really high price tag. You're looking at about £600 for this seat.
Joie i-Prodigi is another isofix option, not quite as nice as the Axkid but much cheaper at £450 (still not a cheap option!)
Besafe Stretch B is seatbelt fitted and costs about £500 but does have a higher weight limit - all three of these seats are up to 125cm height but the Joie and Axkid are 23kg weight limit whereas the Besafe is 36kg weight limit, so could potentially last longer.
Avionaut Sky is the cheaper seatbelt fitted option, £379, suitable up to 125cm and 25kg.
With a couple of these seats (Axkid One, Besafe Stretch) you have the option of the version from birth/40cm, which comes with a newborn insert, or the version from 61cm, which is designed for slightly older babies who can sit in a semi-reclined position with support, usually recommended around 4-6 months depending on the seat. Because your LO is on the taller side for her age but she is only 10 weeks old, you will probably have to go to a retailer and try these out. It will likely depend on the seat whether you can go for the 61cm+ version or the from birth option. The 61cm+ options are generally a bit cheaper - for example the Besafe Stretch (not "B" version) is £479 and the Axkid One2 (not "plus" version) is £550.
In terms of isofix, all cars made since 2013 have it and most cars since about 2006 have it. If the car is older than 1997 (I think unlikely these days?) then it definitely won't have isofix as it is too old. But if you are getting a fixed seat, then it might be worth just getting one seat for your main car and then if your mum wants a seat later, getting a cheaper second seat to put in and out of that.
If £379 is too high of a price tag and you want to look at seats which go up to the 105cm limit, then again you have the option of from birth or from 61cm depending on whether or not they have the newborn insert. These seats spin so they can be used rear facing or forward facing (FF is only from 15 months) and a lot of people like the spinning system. The other advantage of these is that they tend to be stocked in places like Boots, Smyths, Halfords, John Lewis so you may be able to try baby in one a bit easier before you buy.
These ones are a bit more variable and don't always fit a 10 week old baby that well, these are the ones I would say do:
Cybex Sirona G i-size (just one version from birth)
Britax Dualfix Plus (version M from 61cm, or without M from birth)
Joie i-Spin 360 (just one version from birth)
These cost between £220-270 depending on the model, so quite a bit cheaper than the ones going up to 125cm.
Or Graco Turn2Me is only £150 if you wanted a good, budget friendly option, and don't want to spend hundreds (!)
Once those seats are outgrown, you can get a forward facing seat for approx £150-200 or a larger rear facing seat (not suitable yet) for about £220-250.
So if you're sure you want to rear face as long as possible, it does make sense to spend £379 now to save spending potentially £500 in total (or more if you wanted a more high spec long lasting rear facing seat). But if you're not sure or want to make the decision later, then it probably makes sense to look at the 105cm limit spin type seats currently.
Lastly an unusual/rare one to look at:
Recaro Salia elite - this is on offer at the moment on Kiddies' Kingdom for a good price and worth looking at because it comes with a clip out infant carrier which gives you the convenience of the infant carrier you have now with a bit of a better fit. They are even including a pushchair adapter so it's possible (not guaranteed) it will work with your pram. But it's worth checking the fit in your car, because some people say that the angle is too steep and the infant carrier is difficult to clip in and out in some cars if you don't have a big door opening. This goes up to 105cm in the main seat. Recaro is often popular with dads as they make racing car seats. It is a nice quality seat and nice to use.
If you wanted to look at the cheaper, longer-lasting rear facing seats which are only suitable from approx 9-12 months, you could get an infant carrier seat for now for about £100 with nicer inserts than the one you have, use it without any base. This is a good interim option if you don't want to bother with expensive newborn inserts or just like the convenience of carrying a seat around.