When I started working with Salesforce, my colleagues told me that DEV401 is the easiest to get and ADM201 being almost identical to it, but maybe just a little bit more difficult.
However, being myself I was postponing my exam till it was too late to do the DEV401. When I finally decided to get certified, DEV401 was split into 2 other exams:
Being a developer, I decided to try my luck with the platform dev certification. My personal feeling is that you would need some(not much) experience with Salesforce and coding, but it should be pretty doable.
My next certification was the App Builder. It's sort of a new/updated DEV401 exam, so there's nothing about Apex/VF, but mostly just standard functionality(a lot of questions about permissions/OWD/sharing/profiles/roles). Talking to some of my colleagues it looks like the App Builder is a bit more difficult than ADM201, but still very doable.
Also, I know a person who got ADM201, SalesCloud, ServiceCloud and Platform Dev certifications without any prior experience in Salesforce, he just studied for a few weeks and did it.
So to answer your question: you are on the right track, get the ADM201 and App Builder and then you can see what you want exactly.
And you may also want to take a look at SalesforceBen, he has a few tips for the certifications
Yes. As you're registering, you'll enter your payment type. You can enter a voucher/coupon code and/or credit card. This also includes a debit card.
I've paid by this method myself. :)
Best Answer
You will want to use your personal email address (the trailhead one is fine). You don't want to get locked out of your webassessor account in case you leave your current company and no longer have access to your work email address.
If you work for a Salesforce Partner then you can put that you work for a SFDC Partner and also include the company name. This will associate your certifications with your company which helps the company meet partner level requirements.
Otherwise you can just leave it as Customer. And the rest of the options you selected are fine too.