Happy to help!
Doctor/mage are perhaps the cheapest sorts of kit you could go for.
For a physick, a selection of bandages (Boots sell plain wraps, or long strips of shredded old sheet are fairly common), some sort of surgical knives (modelling tools painted or wrapped with something) and several bottles of various things (“potions & lotions, tinctures & tonics”) made from a variety of small bottles and filled with multicoloured stuff, can be an excellent doctors bag. Oh, and a simple canvas satchel to carry it all in 
I’ve played that character, will give details on how to make props if needed.
Mystic Kallevesi mage… right on the brief. You can get some good results from lots of feathers, lots of runes (painted on with acrylics and fabric paint), and maybe some interesting props such as runic stones for fortune telling/augery.
You might also find this of interest, someone playing very similar to your plan…
Boots… I’m spoiled by my work issuing me with sturdy work boots, but any (lightly branded) hiking/walking boots are probably a good idea. You can pick some fairly budget brands, but you want good grip, waterproof, and fairly warm. The April event has an earned reputation for cold snaps, and sometimes even ankle-deep mud. Boots are one of the things to make an investment in, to be honest. Ideally you want something that wouldn’t stick out in a fantasy rpg (black or brown, fairly plain, no obvious logo) but whatever you can manage is likely fine. Some folk say that “kit ends at the ankle”. This isn’t true, but as long as you’re making an effort, that’s the main thing. Not many people will be looking at shoes anyway.
My wife persuaded me a while ago to shell out for the toggi boots below. I play in Dawn so these look good as a yeoman bard/battlemage/peddler.
Re skirmishing: Note that there are two big battles per event, and you’re expected to “monster” in one if you take your character to the other; One day you’re a hero in the battle, the other day you’re one of the barbarians facing the heroes…
However, if you just want to try things out, there’s nothing to stop you having a go as [Barbarian Orc #146] to see what they’re like. A certain amount of kit and costume is provided, and many in your nation will happily lend out a sword or whatever. Something to consider, but the battles are worth seeing
Wider budgets… I can reccomend airbeds, thick sleeping bags, and a sturdy tent with ostensible room for 4 people (larp kit takes up a lot of room). Sleeping OOC (off-stage, in the peripheral fields) is a good first time strategy.
Something like this is likely the smallest I’d reccomend for a pair.
Depending on your travel arrangements, you may also be able to save some money with a little self-catering. There are caterers on site (IC and OOC, a good variety), but they’ll charge. Here’s an older article by… uh… me… going through options.
Oh, and don’t forget that when you book your first event, you can use a discount code for a concession. These are available from any veteran player, who also gets a discount.
I think at this point I’ll let you think for a bit, and let someone else get a word in edgeways