In my opinion, it really depends on the type of activities you want to do in the jacket. Modern uninsulated hiking-type jackets are made at the very cheapest end with some kind of single layer of fabric coated with what they call "dwr" (durable water resistant). These coatings are traditionally made from "forever chemicals", though many brands are moving to compounds that are probably better. Unfortunately, the more eco friendly compounds dont work as well. These coatings, despite the name, are not that durable, so they wear out over time, especially if you wear a backpack. You can replace the coating, but it's a bit of a hassle. Better jackets will have a layer underneath the outside called a membrane that allows water vapor through, but not liquid water. Gore tex is a brand name for a type of membrane, but there are others. This membrane is not very strong, so it will wear out in time, so the best hiking jackets will have a third layer just to protect that membrane.
The paradox with waterproofing is that if you make a jacket 100% waterproof, you will end up wet from your own sweat condensing inside the jacket, so all the hiking jackets are technically only water resistant. Even the best of these jackets will "wet out" eventually and then you are wet anyway. Basically the outside of the jacket gets wet enough that no water vapor can escape past it. This happens faster as the dwr wears out.
If one of those hiking jackets is something you are looking for, look for a jacket that mentions 3-layer construction. Some also advertise a 2.5-layer construction, which is just a thinner inside layer. I wouldn't get too caught up in brands, but just look for one that has armpit zippers.
When it starts to get less waterproof, just re-coat it. Nikwax is the common brand name for the stuff to re-coat, and they are from the UK, so you should be able to find it. Also, make sure to keep the jacket clean. Oils from your skin or any dirt basically clog the membrane and reduce its effectiveness. Nikwax also makes products to wash technical fabrics.
Lately there's been a few companies making jackets out of dyneema composite fabric, which is super lightweight, strong, and waterproof, but they are very expensive. They all also look kinda weird, something you'd want for the trail, but not around town. I don't know how durable the waterproofing actually is because I've never had one.
If you don't intend to use it for hiking, etc, there are different options. When you aren't working up a sweat, it's a lot easier to just have something that's actually waterproof. If you want a good looking option (though not super lightweight), oilskin or waxed canvas are waterproof and can be recoated as needed. Fjallraven Greenland wax is an example of the wax you can use. If you definitely want lightweight, something with polyurethane will be truly waterproof and lightweight.