From what I can understand, Cat 6e does not actually exist but a number of manufacturers are selling some cable labeled as Cat 6e. Some sources say that Cat 6e is just Cat 6a but the manufacturers just added a few extra things to "improve" on it (like shielding I think?). And some say that it's actually some knock off Cat 5e.
I asked for Cat 6a but I got Cat 6e instead. How can I tell if this cable is legit Cat 6 (10 Gbps)?
As you deduced, 6e is a marketing term that was used before the formal adoption of 6a. To correct the term, lets call it enhanced Category 6. The "things" in question that have been modified generally have to do with the physical characteristics i.e. number of twists per inch, separation of pairs and the existence/type of shielding on the cable.
The question isn't really whether 6 vs enhanced 6 vs 6a will -support- 10GBaseT, but rather at what distance. Cat6 is officially rated to go to 55M (including patches) while 6a is good for the full 100 meters/328 feet. This isn't to say, of course, that a 75M run of cat6 won't work - just that it's outside of TIA spec.
Here's the thing, though - if the 5e / enhanced 6 / 6A wasn't correctly terminated on compliant patch panels/connectors/jacks then none of this actually matters all that much. Enhanced 6 should exceed 6 and may be equal to 6A, but the lack of an official spec at the time basically means that you need to base your design on the results of certification with a cable tester capable of measuring to these kinds of speeds. If you can hit 500MHz at the right crosstalk and such (as per 6A) then you're good. If not, then your cable vendor owes you a re-run.
Cat 6a cable is supposed to provide a bandwidth of 500MHz. Some cable analyzers will be able to report on that.
Cat 5e can support full duplex gigabit operations, so in the vast majority of applications even cat 6 is unnecessary at present, but I guess requirements are requirements...
You could use a decent cable tester this should be able to tell you speed. Thus allowing you work out the type of cable that you have.
rnxrx explained the 6a and 6e, so I won't review that ground.
Regarding the new house Ethernet cabling question, I completely agree with your premise, it makes no sense to install 5e or 6 to have problems down the road, Ethernet cable ignorance is unnecessarily expensive. If I was rewiring a brand new house, I would either want one of two options:
6a shielded cabling with shielded connectors. This must be installed properly, with appropriate grounding, and shielded panels and etc..
6a Cabling U/UTP without shielding.
I recently had a new home constructed, and went from the CAT6a of my previous home to whole-house fiber, and provided you have it done during construction it doesn't actually cost much more at all.
I would definitely recommend fiber for in-wall use, the bandwidth is outstanding, and then CAT6/7 for out-of-wall wiring/simply P2P connections where bandwidth isn't the biggest concern, or you're otherwise limited to where 16-32Gbit/sec doesn't benefit (i.e. transferring files from a PC to a simple 2-Drive NAS with RAID1, you will not see any benefit from fiber). However, if you have some serious hardware and need access to large data NOW, nothing beats it (i.e. my basement server room; a single 36-drive RAID60 array buffered by 2 IODrive Fusion-IO 2.4TB PCIe SSD's can push a LOT of bandwidth, and FC was a MUCH cheaper option than trying to go with copper 10GbitEthernet + switches/hubs running everywhere, in fact is was about 1/2 the price overall).
These are an enhancement on the standard CAT6 cables, as they perform much better when installed in an atmosphere with high noise or RF interference. While better than CAT6, they are not just like the CAT6a or CAT6 Augmented standard cables.