Some semi-random thoughts:
Duration: My first two European trips lasted 3 months and 2 months. Later trips were mostly 4 weeks. For the latter part of my career I didn't go overseas because I couldn't get away for more than 2 weeks at a time, and I find trips that short really frustrating. When I got ready to travel again after retirement, it never occurred to me that there would be a problem with a long trip, so I just went for it.
Itinerary Flexibility: Unless I'm traveling to areas where and at times when lodging is difficult to come by, I don't pre-book much before I leave home. I don't know how much time I'll want to spend in a new city until I'm actually there. I often extend my stay; sometimes that is difficult to arrange, and it's often more costly than the original booking, so there are trade-offs. Really long stays are best booked ahead of time, because your chance of lucking into a vacancy for 5 days, a week, or longer is not nearly as good as the chance of finding a last-minute room for 2 or 3 nights. I've stayed in London 10, 12 and 14 nights over the last few years, and those reservations were made well ahead of time--typically early in the 4-1/2 month trip. I also pre-booked Scotland (high-demand area, and I needed twin beds) and Andalucia (around Holy Week).
Saving Money: I do not have a budget. I do what I want to do, but I try to do it as inexpensively as possible. I look for the least expensive, well-located, clean lodgings I can find (nearly always on booking.com) with the features that matter to me: a/c, solid Wi-Fi, and ideally an elevator (or at least not a 5-story hotel without one). As long as my trips are, I'm not going to pay extra for charm. Certainly money can be saved if you have kitchen access; I take advantage of that when I have it, but for a solo traveler the additional cost tends to be significant, so I don't often have kitchen facilities. For a couple staying somewhere for a while, I think an apartment is a good idea, but you have to be careful about refundability, cleaning charges, etc.
I move slowly through the areas I visit; for example, I have spent nearly 4-1/2 months in Spain and 4-1/2 months in France recently. That pace is nearly guaranteed to save money because you spend a lot of time in smaller (usually less costly) cities and won't have a lot of long trips on express trains (which are costly if you don't buy non-refundable tickets months in advance). Small towns tend to be served by regional trains or buses, whose tickets can be bought within a day or two of travel at moderate cost. And the pace of life is more relaxing--important on a long trip.
Investigate options for phone service, medical insurance and evacuation service. Be sure you have multiple no-fee ATM and credit cards.
Managing things at home: All monthly bills are paid automatically by credit card. All credit cards bills are paid automatically from my credit union account. I pay my fall property tax bill months in advance if I don't expect to return home well before it is due.
I travel between early April (rarely) and mid-September. I schedule most medical check-ups for October, February or March, allowing for lab results to come back before I get on a plane and for new glasses to be obtained.
I leave my internet and cable TV service running, primarily because I set up TV recordings while I travel. Many people could disconnect at least the TV service.
Packing: I take one or two pairs of polypropylene or merino wool long johns, a fleece jacket and a rain jacket. I've taken a packable down jacket twice but don't think I've worn it. I only take the pair of (walking) shoes on my feet; most people want an extra pair. Those traveling more off-season would need a full-length, warm coat and probably a long rain jacket/coat.
My main packing issue is the weight of 4-1/2 months' worth of pills. Calcium supplements are especially heavy.