I can only speak from an American experience, so if you're not in america I apologize.
For reference this is my Etsy, and I use Vograce for all my manufacturing! (Except my art prints, I made those with Catprint) They manufacture various acrylic things but I use them for keychains, and their pinback buttons & stickers aren't too bad either. They are a really good place to start if you're trying to break into the merch business. They don't have a MOQ for a lot of products, or it's really low, so if you want to order only a few things you can. It's as simple as making files, uploading to their website, and checking out. There's tons of guides out there and their website is really easy to use and understand, and they have discounts so the more you order the more you save. I've been using them since February and I love them, I've hardly had any problems and the ones I have had are really small nitpicks. The only real downside is they're based in China, so shipping is expensive (but it comes out to only a few cents extra cost per product if you order in bulk) and their English isn't flawless. The reps I've talked to speak it decently enough though, all you really have to do is say "yes, these are good" or "actually, i'd like a change" when they send you your proofs so you don't have to talk to people that much. My last couple orders, it was three to four weeks between placing my order & having my stuff in-hand, so the turnaround time is pretty good!
If you're sending small packages, do not use UPS. The United States Postal Service (USPS) has the absolute best deals for buying labels for small packages (if it's under 1lb (16oz) it's super cheap!), it only costs me $3 ~ 4 to ship my packages depending on destination. Get yourself a shipping scale, it helps so much. Personally I buy my mailers on amazon, I think for me it comes out to like... .10 ~ .15 cents a package, depending on the mailer I use at the cost I buy them at. Make sure you read the reviews, you do not want see-through mailers. Buying them in a cute color is also recommended, so much mail comes in generic mailers but Human Monkey Brain Get Excited When Package Is Colorful so it makes your orders stand out and feel more special when people receive them. i use pink personally, matches my brand :B And I re-use bubble wrap I receive from other packages (we get a lot of mail so i have dozens of rolls of bubble wrap sdlkslakjf) which saves costs a little bit.
I also recommend starting on Etsy if you're new to this, you do have to pay 5% of all your sales to them but it's really not that bad AND!! You get the bonus of being hosted on a website with a search feature. It's a hugely popular website so if you're working on building your brand, it's worth it. When you're setting up your shop you'll need to put in your location, and you can set up Shipping Profiles - these are sort of like templates that will decide how much to charge people for shipping. All you have to do is measure your products weight (shipping scale is useful for this one) and the length, width, and depth of whatever you're sending it in, and input it into the profile. When people check out it will use this information to decide how much to charge them. Damn near all of your orders will be a single product, so it'll only be a few bucks. You can edit this information when it comes time to make your shipping label, though! Then you can print your labels from home, tape them to your package (or stick 'em if you're lucky enough to have a label printer, if you don't have one don't worry about getting one until you've made at least 100 sales i'd say) and drop it off at the post office. Or put it in your mailbox n leave the flag up, if you've got a mailbox. There are many ways to hand your package off to the USPS.
It can be intimidating but there are TONS of guides about opening online shops and how to get started online, youtube helped me a lot personally. I opened my Etsy back in April and it's blown up the last two months :') It's not difficult so much as it is just a lot to do. If you think you can design things that people will want to buy, go for it! It's really fun!