Basic look of my light tarp

I'll add that I use different gear depending on where I'm going and when. I am not going to take my North Face Inferno -20F bag out in the summer in the midwest US.

I do, however, only have 1 "tent" (bivy) that I use year-round (it's a 4-season). I don't take a bivy to be "ultralight," but since I am accustomed to going solo and I don't need a lot of space to sleep, it just makes sense. If I wanted to go lighter, I could skip the pole. But I never feel like I need to do that. I use the Outdoor Research Alpine bivy, which is 4-season, includes a pole (to keep the top from your face and prevent condensation from touching your face), and has loops for stakes (which are not always needed, but are useful in windy conditions). For a groundcloth, I cut a piece of building wrap to fit underneath it.

For cooking, I've been out with someone using a Jetboil, and I like the speed and efficiency. However, I don't like disposable fuel cans. I use an MSR Dragonfly, which can use several different fuel types and connects to a refillable container.

For water, I'm thinking about getting a Steripen. I've seen it in use and I'm told that it works (of course you can't see whether there is bacteria or not), but you still have to filter larger items from the water first (like sand and algae and such). I carry a Camelbak reservoir and I switch to an insulated tube when it is cold. Even then, the reservoir itself tends to freeze up a bit, but there is always a bit of liquid water in the tube. So when it is real cold out, I can't drink water very fast, but I can sip at least.

ETA: I'm not a long-term hiker (though I would like to if I can ever find time). I've not been out for more than a few days at a time.

If you're in the UK/EUR.... get thyself to Iceland!! In all reality, you have a number of great places to go wander in the hills, but for some stunning scenery without the loads of people you oft run into in places like the Dolomites (I mean, still worth it of course) I would highly recommend Iceland.
As for gear.... I've bought all mine in the States so I don't know how much of it crosses over, but if you're looking to do some longer hikes in more inclement weather I would suggest getting a light-weight tent. Nemo, Big Agnes, MSR all making some great stuff currently, but I'm not sure what you have access to. As for other gear... get a mid temp synthetic sleeping bag, while down is wonderful, if you're just getting back into it and will be in a variety of situations a synthetic is a cheaper choice and better if it's going to be wet. I'd go for something rated around -6, yeah, sure it's a bit warm for summer, but for the corner seasons when traveling is cheaper and there are fewer tourists, it's a good option. It's easier to cool down than to warm up. Mountain Hardwear is a good brand for cheaper but quality in the States. Alternatively, buy yourself a less warm bag and get a silk liner to pump up the heat. I have one from Sea-to-Summit that allows me to get away with less bag (about a 9 degree difference. Steripens are great, but once more, it depends where you go. There are a lot of lighweight water filters/pumps out there now (I have an MSR and an offbrand one), and I like the flexibility of being to get water anywhere, whereas the Steripens require less grungy water (unless you like extra fiber I suppose). A small stove is mighty enough, I have one that only cost $50 US dollars, and it's been working for years, packs down to a miniscule amount. Aluminum will serve you well enough for beginning, if you really are watching weight watch for sales on Titanium cookware. Buy a plastic mug with a coffee press incorporated, they're light and a delight in the backcountry. Infinitely tastier coffee than any of the instant mixes. Or, of course, tea is the most wonderful thing as well.

Gearwise.... if you're planning on 7-10 day trips but aren't particularily watching weight, I'd aim for a 65-70 liter pack. Big enough that you can pit everything, but small enough to keep you from bringing your entire household with.

Also, the Gregory Baltero has been winning awards for years for men, I have a number of hiking partners who use it and they love it.

So. That's a lot of text. Enjoy!!

Source: Gets paid to backpack in summer and likes to travel.