adding Wolf Tooth cog to Cassette...What do I need?

I have been researching wolf tooth components and I like their offerings.

I want to get a little more lower gearing on those punchy steep climbs we have in Atlanta. I have a 12-30 Tiagra 4700 (new gruppo), and I am running 2x up front (52-36) 

I would probably need a new Cassette since going from 30T to 40T would be too large of a jump. 

Would an MTB 11-36T 10sp  fit the bill? 

Do I need a road link?  I have a medium cage derailer

Also, I would probably need a new chain since the big-big sprockets has increased. right? 

OR..........

Should i just throw an 11-36T cassette on the bike and get a new chain and leave it be? I am not sure of gear ratios,  but running a 36T in the front and 36T in the back is that ok? Like I said, we have punchy climbs on the bike paths that approach easily 12% or more. 

All in all, I just want to get as close as I can to my MTB gearing I can on my gravel bike. 

Thanks, 

I have not tried it myself but I'm not sure it would work with your current setup. According to this: http://www.cyclingweekly.co.uk/reviews/gears-drivetrain/shimano-tiagra-groupset-review \na long cage derailleur should be ok up to 34. Probably you could stretch that up a bit but I doupt you could run a 40t on your medium cage... \n \nAs for gearing, nothing is more personnal and will varie with your strenght, type of riding and if you're a masher or a spinner. I have 26t with 11-36 cassette on my fatbike, 28t/11-36 on my mtb and I'm currently setting my tricross 1x with a 38t/11-34 xt cassette (i have shimano lx RD). It use to be a tripple but I was 70% in middle gear 39, 28% in taller grear and 2% in granny (probably even more 0.5%) with an 11-25 cassette...

Thanks for the reply. It was getting quiet. I am more of a spinner and would rather spin up the hills than mash. I have been perusing a 1x system. I am more in the smaller ring more than the big. I really only use big rings on descents or trying to get some momentum. 

Drop the FD and just go 1x with taking the rings off has appealed to me as of late. 

 
Absolute black Cx ring. I would have liked to try an oval one but it's not available for 130 bcd spider

Assuming you have the Tiagra GS derailleur here are the specs
http://bike.shimano.com/content/sac-bike/en/home/road/shifting---braking/rear-deraileurs/rd-4700-gs.html
It is designed for a maximum cog of 34. You can probably use 36 without a problem but 40 is not likely to work without a RoadLink.
The other interesting spec is total capacity which is 41T. Your 52-36 up front requires 16T capacity leaving 25 for the rear cassette. The 11-36 cassette is right up against this limit. If you use an 11-40 cassette then the derailleur will not be able to tighten the chain in the small/small combination if your chain is long enough to handle the big/big without breaking. 
Basically you will need a MTB derailleur to handle that kind of range. There is not currently a MTB derailleur that will work with Shimano road 10speed shifters so you would have to use different shifters also. The best option is probably SRAM in that case because their MTB derailleurs are compatible with their dropbar shifters. 
Changing to a 1X configuration would probably allow the 40T cassette with a RoadLink but you wil loose some gear range. Depending on your choice of chain ring you could chose to loose the highest gears to increase to low end range.

You can use a Shimano 9sp MTB derailleur with 10sp shifters. That opens up a lot of possibilities without a whole lot of expense. I run a 50-34 with a 11-36t cassette. A 40t really only becomes a consideration if you're going single ring, in which case you should really look at a clutch derailleur.

To work out what your various gear ranges will be check out this little tool http://www.sheldonbrown.com/gears/ it will show you what your actual gear-inches will be.

Ok so I decided I need to get an 11-34 cassette. Only problem is Shimano only makes one. HG500 (which is hard to get I think) in a 10 sp. 

Can I use SRAM? Looks like there are more options on that side of the fence. 

In one word, yes. All Sram and Shimano 10speed cassettes are compatible. One suggestion that I would have is to use a smaller front big ring. Maybe a 46. That would let you run a larger cassette without chain sag in the small front/small rear gears. On my 11speed shimano 105, I run 46/34 front, 11/40 rear with a long cage rear derailleur and a road link and it works perfect. However with the cost of a 46t chainring, a 40t extender for the rear, a road link and a long cage rear derailleur, you might consider a single front ring. Your problem there would only be the lack of a clutch derailleur possibly causing chain drop.