I've written about three different responses and deleted them all...
Your current Mac can't handle the Blackmagic devices (based on my research). Even with a USB 3 card, I don't think OSX 10.7 is supported any longer and I believe 10.7 is the max OS you can use on that machine.
If you cannot wait: the ADVC 110 will be your best investment at this point in time. You will definitely be able to convert your tapes with this item — to 720x480 DV. Unfortunately, as soon as you upgrade to the iMac, you will lose all Firewire connections (there is a Thunderbolt to Firewire 800 converter available and you'll need the stepdown FW400 converter, and possible the power supply if the power isn't supplied by the TB - FW800 cable) and you will probably lose use of this device without purchasing an external power supply.
There is also much more to think about even with a new iMac.
Yes, you will need at least USB 3 to use the Shuttle and OSX 10.8 or better (probably at least 10.9). If you're going to wait, try to go with the Thunderbolt options.
The other side of the story is that you will also need fast storage in order to capture your video. For SD, you can get away with a "fast" Firewire 800, but you will need something much faster for HD. A standard HD as an internal drive is not going to be fast enough. Research how fast the Fusion drive is — it might be fast enough. I can't recommend an SSD because they're just simply not large enough for my liking.
I built a drive for use with capture: I bought a Crucial M500 SSD drive and put it in an OWC 2.5" drive enclosure with USB3/FW800 connections. I'm getting write speeds of 324MB/s (read @ 400MB/s), which is fast enough for 2K (1556@25fps) but not 1080p60 (10-bit RGB 4-4-4). It was more cost effective than a traditional RAID and if I had a Thunderbolt enclosure (which is much pricier) I could get much better read/write speeds.
[*prices (amazon)
OWC Mercury On-the-go Pro USB 3/Firewire enclosure $55
an alternative type of "enclosure" : KDLinks USB3 / eSATA docking station ($37)
Crucial 480GB SSD 2.5in $180
]
Wait until you get all the hardware in place. You may only have the one chance to recover those tapes (particularly the older ones.) Do it right and you won't be disappointed.
One more thing: if any of your videos are copy protected, you will need to buy a "video stabilizer" to bypass the CP. I personally believe that if you legally purchased the videotape, you have the right to back it up (I am currently supported by the Supreme Court in this opinion; but that could change at any time). If you buy the Blackmagic Mini Recorder (and make sure it's the recorder and NOT it's nearly identical "Monitor") you can get an AV to HDMI converter (from < $20 to about $50 - look for sales) to connect to the HDMI input of the unit.
If all of this is overwhelming, you might want to consider a different way to convert your videotapes, which is to buy a set-top box to do it for you. It will be considerably less work. At this time, there is still a cost effective solution to this and that is a "combination VCR DVD recorder" (the one I linked you to is one of the LAST reasonably priced units.) You will need DVD-R blank disks (100 for ~ $25.) Consider this also: no new Macs have optical drives anymore. Even DVD is passing into history.
Good luck with your project!