IMAP vs. POP - which should I choose?

Would any of tech experts here mind helping me figure out the best strategy for retrieving and organizing my email? It’s a good time for me to find a new host for my website and I’m not sure if I should go with IMAP or POP, or how best to get my laptop and phone well synced.
What I currently do:
My primary email account is POP and I have second email that’s IMAP. Using Mac Mail (v 6.3) on the laptop (10.8.3) and also use an iPhone (6.1.3).
What I’d like to do:
1. Have the phone and Mac Mail sync well:
The POP account doesn’t sync with the phone very well – if I read/reply/delete on the phone, the email in Mac Mail is unaffected, and vice versa.

The IMAP account syncs partially – if I delete an email on the phone, it then deletes in Mac Mail. But – new emails and replies created on the phone don’t show up in Mac Mail on the laptop.

So it seems that IMAP is better for syncing? If so, one point for IMAP.
2. Retrieve old emails from the phone:
I would like to be able to access all old emails when I’m away from the laptop. The webmail for both of my emails is very limited (hostgator and ipower are the hosts) – the old messages don’t stay on the server and the interfaces are clunky at best.

I’m experimenting right now with using a Gmail account as a fetcher for the POP account, which seems to be working pretty well. Since POP is required for Gmail (I think), it seems that POP may be better for online access to old emails? If so, one point for POP.

So what say you, great tech minds? (I’m leaning toward keeping POP with the new host…)

Gmail can either be POP or IMAP:
https://support.google.com/mail/troubleshooter/1668960?hl=en

If you have a Windows machine and wish to archive your email on your home computer:

IMAP is the better protocol. Use it unless you can’t.

This.

POP is a mail retrieval protocol, used for collecting emails from a small mailbox and then storing it in a mail client. It is designed to allow header download, server based deletion and selection/download/removal. It does not support multiple client access, and was intended for dialup and low bandwidth use.

IMAP is an email access protocol, used to access emails stored in a permanent mailbox on a server. It supports access from multiple clients, and has a variety of email management features. It is far superior and much more capable than POP. It is almost always the correct choice.

One of the very few things I hate about Thunderbird is that its automatic server setup is very difficult to override, either during account creation or later. Because my email usage has always been complex and is getting complexer right now, I’d like to try IMAP for my major accounts. But if there’s a way to set up an account for IMAP (before the automatic process sets it up as POP3), or a way to change an account to IMAP later, I can’t find it.

The only issue I have had with Thunderbird is convincing the setup that I am using a gmail address (as a reply to) with a private server. And my setup is pretty complex, with IMAPS and private certificates and all. I’ve never had it try to set up POP, though.

Missed the edit: I just checked, and it appears they’ve improved the account setup method. The last time I tried it, it was somewhere between impossible and requiring of superhuman reflexes to hit the “manual configuration” button before the automatic process decides, By Gum, that you’re going to get a POP3 account. I was able to easily hit the manual and set up the account.

Now I just have to think about converting eleven active accounts… sigh.

Ninja followup: I’m not trying to set up a GMail account. I have one because you can’t function (especially in the Android world) without one, but my accounts are all on private hosting. For whatever reason, they’ve always quickly defaulted to POP3.

No one has commented on this. OP check your settings and see what server you use to send the mail out on your phone. For example if you are using the cell phone company to send out email, then it is not going to show up on Mac Mail. You would need to use the Macmail server to send out email for it to show up on Mac Mail.

Pop3 don’t forget to turn on the Leave e-mail messages on your e-mail server option. By default messages are deleted off the email server. That can ruin your office email if you also read it from home. Office email is supposed to be on the machine at work and not stuck on your home pc.

This is a client setting, nothing to do with the outgoing SMTP server. You need to ensure that all the clients use the same IMAP folder for Trash and Sent Mail - most clients tend to use local folders by default, which is rubbish.

I use IMAP for my main mail accounts, and I really like it, but beware… at least twice over the last few years, I have had something (some unknown something) happen that wiped my inbox on the server. Since all my machines are synced, this resulted in all my messages in the inbox on all my devices getting wiped, too.

I use Time Machine to back up my systems, so rebuilding my mail wasn’t too hard, but I did lose a bunch of messages that day (they came in between backup intervals and the unexplained event).

So be careful - if your email is important to you, keep a local copy, in addition to the copy on the server.

(As an aside, I had a client have this happen to her, too. But in her case, I figured out what was happening. Turns out, she somehow launched Outlook, and it was set to use POP, with the same server parameters. So, it dutifully downloaded all of her email, and then deleted it from the server, which wiped everything in her mail Inbox.)

My method is to turn off “Delete messages” on all clients except one master, which is set to delete messages on the server after 7 days. For all the advantages of IMAP, this has worked well, allows me to delete messages from my phone with impunity and provides a degree of automatic backup among the clients.

The bottom line is that I don’t trust a third-party server with any of my data, email especially. I’d rather pull in, manage and archive it myself.