In my experience, Hunter Paces can be fun, but aren’t much like hunting; to me, they’re more like a regular hack in good company, with the added bonus that I don’t have to bring lunch!
Even though you (OP) aren’t planning to hunt until the autumn, it might be a good idea to attend a hunt or three on foot. Some of our coolest oldest hunt members still follow hounds by car, and welcome newbies, which is a wonderful and informative stress-free introduction to all the minutae of hunting. With any luck you’ll meet some of these older wiser people, who’ll scoop you up and spoonfeed you with the best they have to offer. 
Just check it’s OK with the secretaries of whichever hunts you plan to attend.
About fitness - the old adage about allowing 8 weeks holds true, ie, from pulling muddy unfit pony from grassy field, to being able to sustain a brisk trot/canter for a good hour without puffing hard (both of you!). If you can stand in your stirrups for all that time, so much the better. The Pony Club manual used to lay it out pretty well.
I strongly disagree with whoever says you don’t want your horse fit; that’s inviting trouble with unnecessary aches, strains and stresses on heart, lungs, limbs and mind. Same applies to the rider 
- the fitter you are, the better able you are to ride your horse effectively, and enjoy the proceedings without passing out from exhaustion! Feed according to work, and your horse will hopefully be manageable within its normal boundaries.
Even though you won’t be hunting for a while, you can practice stuff like teaching your horse to stand still for 15 minutes or so without fussing, waiting while the others go ahead, going ahead without the others, leg-yielding, etc: basic old-fashioned group manners that aren’t always required in modern show horses, but are still to be expected in a good hunt horse.
The Hunt may suggest you go out with them on hound exercise, which can be instructive, but do check first how long they’ll be out for, and what pace they go at - I’ve seen hound exercises that depart the kennels at a brisk canter, much to the dismay of the attending newbies!
You are going to have SO much fun. :yes:
PS About your boots - search Ebay UK - riding boots there often have fatter calves :rolleyes: go figure (Regent is a decent-quality British brand that seems to come in larger calf sizes). Alternatively, find a good used pair that have the correct foot size, and have a good cobbler put a gusset in down the back and/or trim down the height so they’ll fit you perfectly. I prefer to buy quality used than cheaper new, if that’s any help.
