Find your local comic shop and check it out. Look around, see what you like. If they are good shop, they have a current issue for each comic to check out the inside versus just seeing the cover art.
If you like a few things, see if they have what is called a "Pull List" or "Subscriber List". This is where they set aside the comics on your list every week so you can ensure you get them and pick them all up at once, often at a % discount. A good shop will not charge you for "bag and board". This is the cardboard backer and sleeve your comic gets put in to protect it. Usually made from acit free materials, often by BCW. If they aren't doing this, or are charging you for this, maybe look into a better comic shop.
Every month, there is put out a "Previews" catalog that shows what is available in the next two months. It's like $5. If you find yourself getting into comics heavily, picking one of these up monthly is the way to stay on top of your game.
Lastly, you'll want to pick up a short box or long box to put your bagged and boarded comics into to protect and store them. Most shops should carry these cardboard boxes for a couple bucks.
Some good series I like:
Anything with Superman
Anything with Batman
Flash
Star Wars Darth Vader
Star Wars Thrawn
Green Lantern Corps
Black Betty
Walking Dead
The Boys (finished several years ago, but the graphic novels are available, amazing series)
Locke and Key
Most of the Marvel stuff should be avoided until they are done cleaning out the SJWs that tanked their sales. They just aren't good, unless you are into that. Give it 6 months or so to see if the ship is righted.
IDW has hits or misses, but they are seriously hurting after taking a severe left turn and losing 91% of their sales, just fired their president for shens, and could be losing the Hasbro licenses this year.
Image has hits and misses as well. Both are worth checking out for some good stuff hidden among the dying SJW tripe on it's way out.
As always, check out the indie titles for great stuff.