OP wrote:
"I ask because I don't know if the 250GB SSD in the LaCie can be replaced with a bigger drive in the future."
I've heard of others doing this. You have to remove the "rubber bumper covering" from the case, then you can get inside the case and do the swap. Disclaimer: I don't own one of these drives myself -- that's just what I've read from others.
"Also, I've read the USB3 port on the LaCie isn't the best."
The important factor is whether or not the LaCie enclosure has UASP support. (USB attached SCSI protocol). A USB3 enclosure NEEDS THIS in order to run at the "full speeds" that are possible with USB3.
"And do newer Macs have Thunderbolt connections? Or is Thunderbolt a dying breed?"
Right now, all new desktop Macs and most MacBooks still have the thunderbolt port. I sense that in coming years, we are going to see thunderbolt eclipsed by future versions of USB (USB3.1 will be arriving soon).
But this isn't pertinent to YOU right now.
Your original question asked for the best way to get a new drive working with an iMac that had thunderbolt but NOT USB3.
I believe your best course of action would be to connect a thunderbolt-based external drive -- quick and easy, and you don't have to mess with "going inside".
You should be able to get at least 2 more years of "good use" from the existing iMac this way, and I wouldn't be surprised if adding the thunderbolt external drive really "perks the machine up" speed-wise.
And sooner or later, you're going to get another Mac. If the LaCie drive has both thunderbolt and USB3 ports, it's coming with enough "forward-facing insurance" so that it will remain a useful peripheral with the newer Mac, as well...