Best resource is to find a garden club in your area, or the county agriculture extension.
Might be a good idea to just go to a local plant & garden shop and compare what they sell with what you see. Such a store will also probably give advice on how to care for anything they sell.
Also a good idea to ask your neighbors!
I deal with mostly a vegetable/herb garden and a native (to my area) flower bed, so my experience with gardening comes from that. I don’t recognize a lot of the plants in your photos so I can’t give a lot of specific advice. However here’s what I know/noticed:
Dead stems: Yes you can cut off the dead stuff from last year’s growth. I cut them as close to the ground as I can. I wait until spring because it makes a good winter home for butterflies and other helpful insects. Plus if the flowers make any seeds birds and other animals can eat, leaving them until spring gives the animals some extra food during the winter.
Weeds: What is a weed will greatly depend on the area of the world you live in. Several photos have creeping charlie in them. Creeping charlie is the stuff growing low to the ground with the purple flowers in image 4272. Creeping charlie isn’t native to my area, so I pull it because otherwise it creeps into wherever it can reach (which is everywhere). I would keep an eye on image 4261, that one the leaves look somewhat (but not exactly) raspberry/blackberry species which can be welcome or can easily take over. However I will say the stems aren’t what I’d expect for a raspberry species.
Plant species: 4253: The leaves and stem are saying columbine to me. 4254: The tall leaves could be some kind of day lily or tulip like the flowering ones in 4275. 4259: Bleeding heart is in the upper left corner.
Hopefully someone else will recognize more of the plants so you can find out exactly what you have.
I see some hostas coming up, and a bunch of other perennials.
The dry woody/dead things can probably be trimmed back with sharp scissors or garden shears.
Pick up any leaves/sticks on the garden bed, and you should be pretty okay to start.
It's hard to tell if some of the stuff coming up are weeds or "good" plants (I personally think some traditionally considered weeds can be quite pleasant - looking at you tickweed).
Let it grow out and don't do much this year. If you don't like what's there, next year you can start ripping things out.
Find an app like Seek by iNaturalist or some other plant identifying app to help with figuring out what things are, and when things have grown a bit more, take additional pictures and take them to your local garden center/nursery for help with specific plant care/identification.
I'm not in a position to look at your photos right now so I can't help you with your immediate question. I was just going to come here and recommend you to take photos of your garden and don't do any major changes for the first year. Knowing what things look like during all seasons help you with planning your gardening going forward.
If you keep up with the obvious weeds and work slowly to identify and read up on the other plants I'm sure you'll be in a good position for year two. And if you accidentally remove a plant that isn't a weed it isn't a big deal - it just gives you the chance to choose your own plant for that spot.
Take your time and wait. Know that learning to garden is a matter of trial and error. I like the iNaturalist app to identify plants (and animals and insects and...) so that should help you figure out what's what. A lot of young or early plants are hard to identify, but you'll pretty quickly learn to recognize your frequent invaders. As for the dead twigs, I like to leave them until late spring so I know if I should expect something else to come up, then either leave them if they're little or cut them back if they're an eye sore. Some plants that are supposed to die back may not if the winter is mild enough, and some plants that aren't supposed to die back might if the winter is severe enough. Some plants will also die back in a particularly harsh summer.
All of that go say take your time. Even the worst "mistakes" are easily fixable.
I can't open the photos, but a lot of perennials die back and grow new stems. You can probably cut the dead bits off. If you want to be sure, give it a little scratch near the base. If it's green, that part is alive, if it's brown, it's dead.
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