I have no experience with doing what you're talking about per se, so the advice I can give is from the point of view of an extended hike in camping trip. I'm also going to assume you don't know anything about camping so I will be possibly over explaining things l.
The first thing to consider is the weather in the area you are going to be doing this extended vacation. Is it going to be hot or cold? This will dictate what you wear and what you take. If it's not very cold where you're planning to do this you can travel much lighter as the majority of the weight on a hiking trip goes into your bedding and shelter. For example during the summertime I can get away with comfortably traveling with just a covered hammock and a 40°sleeping bag for a combined weight of about 2 lb. However if I expect the weather to go below 40° I am taking a zero degree bag with a mat to keep me off the ground and a tent, which is a combined weight of probably 7 lb. That doesn't sound like a big difference but the rule of thumb for when you are hiking is that every ounce feels like a pound over the course of a mile hike or farther. And with betting especially The bulk of all of your items necessitates carrying a larger pack which is then also heavier and adds to the amount of weight you have to carry.
Speaking of bags, military surplus bags are always nice. I recommend something with a pack frame, you would be surprised how much that helps. I personally recommend ALICE packs, they're very very nice. last I check you could get surplus ones for around $70. However those I've been out of production for at least 20 years and are getting more difficult to find and if you don't live in America I don't know how easy they are to get where you live in surplus variety. There are companies that make reproductions that are very expensive, to the point of being price competitive with the higher end hiking bags. M o l l e 2 packs and pack frames are fine, but I have yet to come across a surplus molle 2that had a functional belt.
since you are going to be walking a lot it is vitally important that you have at least and I cannot overemphasize that you definitely need at least two but ideally four pairs of high quality boot socks, SmartWool is a well-known high quality brand, because getting blisters is going to ruin the whole experience. Additionally high quality hiking boots are going to be a necessity if you're going to be doing a lot of walking. I don't know what your budget is so I we'll just say that in general I cannot recommend a booth that cost less than $60 and I can only recommend one boot at the absolute lowest end which is a rothko Vietnam jungle Boot replica, which would only be good in the summertime, it literally has holes in it to let moisture out so It would be completely unacceptable as a winter hiking boot. If you can get other genuine military surplus boots from first world countries those are generally going to be fine but I can't say absolutely that is a case across the board. Getting into the mid-range boot Merrill is a very good brand for the mid-range, and then keenes or Salomon's a really good on the upper end of the price range. I recommend getting a boot that have a shank. A shank is just a piece of metal in between layers of the rubber in the bottom of your boot, you would be surprised at how much more comfortable it makes the boot.
If you can find lined pants those are really really nice and cold weather but they are not always the easiest thing to find
A mess kit would be nice to warm your food, you can get a stainless steel mes kit that is perfectly fine at any Walmart assuming you're in the US, but I'm sure there are equivalent really simple and cheap stainless steel mess kits regardless of where you live.
Fire starting materials are always nice, can't go wrong with a ferrecerium rod, or a lighter, even an empty lighter of the classic kind can still be used to light a fire with the little sparky thing.
Two large and durable water bottles is usually a good idea. You need a lot of water and it would suck to run out of water because something poked a hole in your only water storage device.
A camping ax is something always nice to have, the light or the better You're not going to be chopping logs down or trees down, just coming up enough stuff to make some kindling.
Last but not least a first aid kit is very important. Bandages splints antiseptics anti-inflammatories tourniquet tweezers bandage rolls needle and thread for stitches.
When having something to sew up holes in your own clothes maybe a good idea or to put patches in
