I have two of the Mid 2011 27" iMacs, and this is by far my favorite iMac to do mods to. So many options to do for internal and external drives too.
This is the only non-Mac Pro Mac that you can have three internal SSDs. I installed a SW RAID0 in one of them, with a third SSD for Windows, all internal.
One of the few Mac models that you can swap the GPU in.
Fast, great display, and just a really good Mac.
Get rid of that HDD. They run hot, and many people believe that the heat from the HDDs contribute to the high GPU failure rate for the Late 2009 - Mid 2011 models.
As for a SSD boot drive, you have so many options with this Mac:
USB2 - Slower than internal. about 40MBps max speeds. No TRIM support. Really cheap option.
SD Card - I think this is connected via USB2 IIRC, SD cards expensive, and not worth it imo, unless you already had one.
FW400 - A little slower than USB2. I wouldn't bother.
FW800 - About twice the speed of USB2 @80MBps. Not bad, and probably wouldn't feel too much different than a 10 year old HDD. Sequential speeds are much higher with a SSD via FW800 than a HDD internally.
USB3 - Get this via a TB dock. About 350MBps max. Will feel much faster than the internal HDD.
TB1 - A SATA SSD would be about the same speed as a USB3 SSD, but you get TRIM support. Hard to find these drives, and eBay would probably be the best way to source them.
TB2 - Basically the same as the TB1 drive on your iMac. You can also find some NVMe and AHCI TB2 SSD enclosures. They tend to be pricey, but you could see speeds close to 800MBps on the NVMe TB2 drives that I have researched before.
TB3 - Requires Apple bidirectional adapter. Depending on the set up, could require a TB3 dock to power the drive. A TB3 NVMe drive is the fastest single non-RAID drive you can get for you Mac. Speeds over 900MBps, but at a cost. NVMe drives are falling in price, but between the drive, the bidirectional adapter, and maybe something to power the drive, this could be an expensive option. Also has TRIM support.
Internal - Has TRIM support (you got to enable it), fastest SSD option besides the TB3 NVMe ones. Cheapest option. Opening your iMac could be intimidating, and you could cause dmg, but it really isn't a big deal to anyone with a little computer experience. You will need a SATA temp sensor adapter or use SW to control the fan speeds. Macsfancontrol is free. I recommend a SATA 2.5-3.5" drive caddy, but not required. About 500MBps speeds.
Internal would probably be the best way to go, because not only is it cheap, but it is fast, and clean set up and has TRIM support. You can also get that hot HDD out of there as well.
I have done this many times, and no lie, I could probably do the internal HDD to SSD swap in less than 5 minutes.
I am wondering if just using the new SSD externally instead of opening up this thing would work?
Yes. Many people boot from externals. I do on one of my Macs, and have for years.
Right now I am using it this way but it is very slow? It is hooked up with a USB 2 ... prob why it is so slow?
Depending on what you are doing with your Mac, most likely yes. You are probably only getting about 30-40MBps for sequential speeds.
If you have a SATA FW 800 enclosure, that would significantly improve things over the USB2. Not as good as internal, TB 1/2/3 or USB3, though.
A SSD over USB2 should have faster random speeds over your internal HDD though.
Can I hook this SSD up using Thunderbolt port and cable? I assume this would make it faster?
Yes, but TB 1/2 drives are more expensive and harder to find. You would have an easier time getting a TB3 NVMe drive. Doing a TB3 set up might even be cheaper depending on the deals you find for he TB 1/2.
You could also get a TB 1/2/3 dock, they usually have USB3 on the dock, so you can just use that to boot from.
Would it be faster if I installed it into the machine (replace the old HD)?
Yes, much faster.
Or would a Thunderbolt connection and use it externally be best?
Better than USB, and has TIRM support, but more costly. Depending on the type of SSD and if it is TB1, TB2, or TB3, the speed could be any where from 300MBps to 900MBps max.