Rushes make great shelter for lambs. So if you are planning on breeding sheep, do not remove all your rushes - the amount in your pic isn't much
and would be just right for shelter for the lambs of the 3-4 ewes you might have on your 1.5 acres.
Rushes also help bind the surface together, and use a lot of water, so if the ground is wet and the climate also, rushes could be more of a friend than a foe. Just top them in the summer, twice if you can, to stop them getting out of hand.
Permanent pasture is by far the best at withstanding weather extremes, be it drought or prolonged wet. Do not plough and reseed without a lot more knowledge, and local knowledge. Talk to your nieghbouring farmers, they will know what will and will not work on your patch.
If it's wet land and you do plough and reseed, you may find you can't run any hooved feet on it for a couple of years while the new grasses get established. Same may apply to more than three or four choox.
I think you've received the messages No Ponies, Never a Single Cow and Not Enough for Two Cows. Sorry!
But... once you are known and, hopefully, liked!, you may well find that there are ponies about locally that are underused and their owners very happy to have an experienced rider make use of it/them. It's Fell Pony country, it's a breed that loves to work.
And once you have got used to your new spot for a year or two, and had a few choox and maybe a couple of weaners, and know people locally, well then you may find there is summer grazing around you could use for your two Shetland cows. Depending on exactly where, you may need to lead them home for milking, or milk them in the field.
I have Jersey house cows, which produce so much milk I have to buy in calves for them to rear alongside their own, so they hardly notice what I want for the house! I'll share a few things I've learned. If a cow is rearing her own calf then yes, you don't have to milk her every day for her own welfare -
but I find it best to mostly keep the routine the same, especially in her first and second lactation, so I do try to milk them every day for at least the first lactation. After the first couple of weeks, you will need to keep the calf off her at night, so that she has a full udder for you to take your bit before reuniting mum and calf in the morning. You can't keep a calf on its own, nor a cow on her own, so the solution is usually that the calves are penned together overnight and the cows run out or are penned together but away from the calves, whichever suits you best. You can have them in pens next to each other so the mums can see and talk to the calves but the calves can't reach the udders.
The other thing I want to share is that you will form an amazing two-way bond with a cow that you milk. I was unprepared for the strength of this bond; it's as strong as that with a horse or pony that is yours and you work/ride. It's a wonderful thing, for sure - but it does mean that you should take the step of getting a couple of house cows very carefully. If you rush into it, then find it isn't working for you, your land, or whatever, then you will have a heartbreaking situation to deal with. Probably it's not terribly difficult to rehome a couple of trained Shetland house cows, but it would still be a wrench for whoever milks them especially but also for the whole family.