Whoops, sorry I forgot to answer that part. I understand that the SSD-only iMac models, although they have a space, don't have the cabling and brackets installed to take a secondary drive. I am not sure how easy it is to get those components and install them successfully, but it's certainly more involved that just swapping the drive that's already there.
Well, here you go:
https://www.ifixit.com/Store/Mac/iM...-2014-and-Mid-2015-Hard-Drive-Cable/IF174-006
Brackets are already installed.
iMacs don't just take any old SSD (at least not in their primary drive space, although you could replace the second part of a Fusion drive with SSD). They take very specific and much faster cards that are not compatible with anything else, even across years of the same model. That's part of the reason that a 1Tb SSD iMac is a way bigger jump than the price of a normal off-the-shelf SSD drive.
The "specs you ask for" are a specific Apple SSD card for that particular machine. They can be bought, but you are unlikely to find that the price of one of these plus professional installation is going to save you anything. And, of course, you open yourself up to warranty issues in the future.
The SSD in an iMac is not intended to be upgraded. You should ideally buy the one you're going to need, and use Thunderbolt to connect additional storage as you require it.
Time Machine can back up multiple volumes, and you can restore them to your new machine as required, as long as each new volume is as least as big as it needs to be to take whatever you're putting there.
Yes, an Apple service provider will be able to provide you with a price to put an SSD into your 2013 iMac.
For the OP:
SSD that comes with the iMac is proprietary. You can find buy one, but it's going to be expensive because it's proprietary.
What a lot of people do is that they buy a standard SSD and put it into the hard drive slot.
Oh, and the OP
don't need to go to an Apple authorized service provider: plenty of third parties can do the upgrade.
Heck, I can do it for him if he lives anywhere near me.
More questions...maybe nothing more than curiosity but still I'd like to know:
"Any of the SSD only model doesn't come with the hard drive" but one can still put a hard drive in if one wishes, right?
Is it worthwhile to get a 1TB SSD right from the start? Can I upgrade the SSD anytime later? If I can buy a 1TB SSD from my local memory specialist for much less (what specs do I ask for?) than what Apple charges that would be appealing. Can an Apple service provider install SSD that I have bought elsewhere without problem? Is any brand of SSD better than the others?
The SSD that Apple uses in the iMac is proprietary and while you can buy one, it is really expensive. Anyway, I recommend just getting the 256GB SSD with the iMac. You can store most of your data on the hard drive (that you are going to install afterward).
What a lot of people do is that they order the hard drive only iMac model and then replace the hard drive with a standard SSD, but that won't work for you since you also need a hard drive.
I'm thinking of keeping my 2013 iMac and taking it to our soon-to-be office for business use. Can I have the Apple service provider install an SSD into this older iMac without problem? Is there a max SSD size for this older iMac? Where do I go to find out the specs for an SSD going into a 2013 iMac (presumably different specs than for a 2016 iMac)?
Absolutely! You can install as big an SSD as you like, assuming you can afford it. (4TB Samsung 850 EVO is $1450

) It's going to take place of your hard drive, though.
You can also install Apple's proprietary SSD, but it's going to be expensive.
Also, you don't need to go to an Apple Authorized Service Provider. Plenty of third parties can do the upgrades for you.