You have no problem with space UNLESS you try to keep twenty copies of the entire site and database on the server. Then, it's a definite maybe. One host that starts with #0000ff offers unlimited storage for all but the basic plan. 50 GB for the basic. One of our sites with 24 main categories, numerous sub-categories, and over 2500 product IDs is using less than 3 GB of space on the drive. And they have three complete sites for testing while running 5 databases. In May, their biggest month of the year, they used only 20.5 GB of bandwidth. This while doing $78K of business at $65 per order. That's just under 1200 orders.
As of two months ago, the host with #0000ff was still removing the cPanel option that allowed a customer to do a backup. They charge instead. They charge for dedicated IP when they are only needed for mailservers. Rather than keep the bad boys away (loss of money), it looks like your former host just wanted to make extra and talked you into the IP versus fix the real problem.
We even had one host who we had to take legal action against to get them to release the customer's images and files. They claimed they became their property when they were placed on their server.:(
Most servers/hosts advertise providing numbers that they know you will never reach and leave out the little things they know you will need.
I like to think of it as advertising an eight-person SUV and finding out after your purchase that you are responsible for providing the extra six seats. You thought they were folded under the mat when you purchased it.:(
On the subject of TTI (Time to Interactive), you will find many variations of what is a good score. It's not a standard in the web world at this time as not all monitoring tools use it. But it makes complete since that, if your site is not "ready" in a certain amount of time, folks will leave. More so on a mobile than a desktop. Unfortunately, most folks design for a desktop and, as you mentioned, may not have the images managed for mobile. You can really delve into it at https://www.holisticseo.digital/pagespeed/tti/ You should bookmark this one as it is a treasure trove of info.
You'll note that the above tti website lists 0 - 3.8 as Fast, 3.9 - 7.3 as moderate, and anything over 7.3 as slow. The site mentioned above with 24 main categories is getting 1.1 seconds with Chrome's Lighthouse Desktop test. On the mobile side, it gets a TTTI of 3.7 seconds. When they take the time to properly size the images for those 2500 product IDs, I'm sure that number will drop. There are other options available as mentioned on that tti website, as well.
Note that the site is using a fairly standard responsive_classic template and no slideshows. Another customer with an even more complex template is showing 0.9 and 5.1 respectively. They use larger images but they are managed more for the desktop.
Note also that these numbers are relative to the speed of your connection, what images are being displayed at the time of the test, etc. Another thing to consider with a host -- what size port do they use both coming and going. Trying to force a thousand gallons of water through a 12" pipe is a lot easier than through a 2".
So, to get to the meat of the matter. What you are stressing over is the last thing I would consider with a host. I'd want to know how often I can back up my own site. Maybe a simple action but, so many are not offering it at no charge.
What other things can I do with my (insert cPanel or equivalent here)? Can I create sub-domains? Can I virus or malware check my site? Can I manage my own PHP settings (VERY important if you are going to upgrade or test on that server)? Surprisingly, some hosts still do not supply email accounts with their lower packages.
What do I need to do to get a free domain registration and/or free SSL? What is their rating at https://ssllabs.com/ssltest/? As of 18 June, only 1.7 percent of sites tested had an A rating. No figures are available as to how many A-, A, or A+ in that group. 50% of all tested were still supporting EOL SSL protocols that force them to a B rating at best.
Are there any other platforms with me on the server that are prone to hacking? If I'm told I will be on a server with WordPress, I'm running in the opposite direction. One site that admittedly sells hack-cleaning software touts that "10,000+ WP websites are hacked daily & marked as dangerous with a Big Red Warning banner". In October 2020, that #0000ff host announced that six popular WP plugins were hacked. This is where I pass on kudos to swguy and his work as moderator for ZCs plugins.
I'd want to see an example of someone running my software on their server then Google a competitor to see how the statistics match up. It's NOT the responsibility of the host BUT, it will give you an idea of host performance. Especially in the TTI area.
Best of luck in your search. Hopefully this helps in what you should be looking for. I realize it is lengthy but knowledge is power when you shop.