A general answer to a general question
Long distance through hiking is a fairly well developed activity in terms of common best practices. I would suggest picking up a book on more popular through trails (The Appalachian Trail or Pacific Crest trail in the U.S.) that has many handy suggestions. Take from it what you will based on the terrain you will cover.
Choices vary significantly on your hiking philosophy, The Ray Jardines out there will say that you need to go as light as possible, bringing only a poncho for rain protection (both sleeping and hiking) and a sweater as a ground cloth, hike in sandals, backpack over one shoulder, etc etc. the more old-school expeditioners will rely on heavier packs and gear to be ready for everything and just deal with the weight. The modern athletic through hiker brings state of the art light-weight everything to combine both for a cost.
Essentially all you really need is a pack of some kind with food, and footwear. Depending on the conditions/terrain/country you may need or want to bring a tent, water purifier, stove+cooking equipment, navigation (gps/maps), snow/ice gear, entertainment. You may not need everything the entire time so your resupplies may require gear drops/pickups as well (for instance, early/late season PCT through hikers usually send themselves crampons and ice axes only when they get to the mountains, to avoid dragging the weight through the desert)
Through hikes are typically separated into "sections" between resupply points. Nobody carries all their food on them the entire time, and people exit the trail to hike out to a nearby town (or the town is on the trail) to purchase supplies, relax, do laundry, etc. In certain areas it may be necessary to ship yourself supplies because there are no general stores available to purchase food and gear. It is important to identify those sections and plan ahead. Some areas it might be possible to hike from town to town and sleep in hotels, other areas it might be necessary to hike a week or more in the wilderness.
Europe is a fairly well developed place compared to the western american wilderness, It may well be possible to hike through without much issue by going town to town and maybe skipping sections by hitchhiking or public transit with the most difficult parts in the eastern rural areas, without being familiar with the trail I wouldn't know which sections would be the most wild and which the most urban, but I suspect the trail is most likely very similar to the Appalachian trail with historic foot transit paths interconnected with constructed wilderness trail sections. The easternmost section hits the balkan mountains and is probably your most difficult section
Your average through hiker will typically do 15-30 miles ( 25-50KM) a day on flat terrain, dropping to 10-20 (20-40km) a day in mountainous terrain. When I hiked the signficantly shorter John Muir Trail, we were pushing 30-40 km a day with 1000-1500M of elevation gain every day, many of the longer distance through hikers did the same. Keep in mind that this doesn't include "zero" days or shorter days for recovery, which will drag your average down significantly.
What limits you more than your vacation time is your weather window, you will likely not want to hike in winter, early spring, or late fall so your choice of route direction and time frame will be dictated by this. Making sure you pass your colder/taller areas in the summer to avoid winter mountaineering conditions
You need to plan for food expenses (budget 1.5-2x your typically monthly food bill), Gear replacement (you will go through several pairs of boots, shirts, pants, and socks), lodging, laundry, public transit (if you need to taxi,bus, or train out to a major population center for resupply), and extraneous (posting yourself your gear/food if necessary). It is very difficult to do a long trail like that as an athletic wilderness adventure, spending more than a week out in the wilderness takes a hard mental toll on you, and many through hikers treat the hike more as a tour of the area, taking their time in cities and towns along the way to relax and recharge, drink beers at local bars, etc. When doing long through hikes its amazing how appealing a bottle of beer or an ice cream bar marked up 3 fold is after being out for 10 days straight.
It is probably a good idea to purchase some kind of adventure insurance in case you require rescue or evacuation. I know for a fact that joining the german alpine club gives you evacuation insurance up to a certain amount as does the american alpine club, there may be similar clubs or associations where you live to do the same.
A smart phone with a gps and maps app, and a solar panel to charge can replace a gps reciever, extra batteries, and a stack of maps. Many AT/PCT through hikers have this set up, when it rains they place the phone in a plastic bag and can still use the screen while keeping it dry. This can also double as your nightime entertainment (download movies/tv shows when in town) and emergency communication. Additionally, a spare phone is not more expensive than a new gps receiver, the extra batteries, and map software for it