Hi Sam,
Welcome to the forum and welcome to the best sport/ outdoor activity under the planet.
Unfortunately the current coronavirus situation makes this far from the ideal time to start caving for two main reasons, 1) Most clubs are currently not organising trips and 2) Cave rescue services are operating under difficult conditions and a reduced pool of volunteers. Current advice from our national bodies (in addition to government guidance) is to take extra care and remain well within you own ability. Personally, I would worry that if you are new to caving, it would be very hard to judge what you level of ability is and therefore where might be an appropriate place to visit. I think most cavers who are going underground at present will be visiting sites they are very familiar with, rather than breaking new ground so to speak.
On this basis, I would strongly advise you to wait until this is over before venturing underground.
That said, I'm not your mother and this is a free country, so if you do decide to go crawling into any holes in the ground, I would urge you to take particular care as there may be unexpected dangers that you are not aware of.
Once this is over, I would seriously consider joining a local club, who will be able to safely introduce you to the many aspects of caving, including SRT (single rope technique) used for vertical pitches. Clubs also have a good supply of equipment for members to use, so you don't have to go out and buy hundreds of metres of rope
In the meantime, if you do decide to go underground, in the Dales, you would probably enjoy the entrance passages in Valley Entrance in West Kingsdale (as far as the 1st pitch, but please don't try to descend this without proper equipment, or you will end up in trouble), or possibly Mistral Hole in the Ease Gill system, if you don't mind a bit of squeezy crawling on the way in/ out. Wretched Rabbit (also in Ease Gill) may also be suitable if you have good upper body strength for the entrance climbs which have a fixed handline, but please be aware that this cave provides access to an area of the system that floods completely in wet weather, the system also involves some very complex route finding, so do not go too far in one trip; better to explore a small bit at a time as you learn what is what.
Obviously refer to the CNCC website for latest access details (which may well be different to usual) and cave descriptions
https://cncc.org.uk/caving/
I can't speak for the Peak as I don't now the area...
Whatever you decide to do, do your research, take care, turn around if you are in any doubt and let someone responsible know where you are going and when you expect to be out. Finally, remember to be considerate to the local population in caving regions, as damaged relations will take time to heal...
Stay safe.