How do I choose the correct airfoil? I am currently working on a personal single seat, piston aircraft that I would fly myself and I am currently in a bit of conundrum when it comes to my wing design. In this project, I assigned us in 2 basic groups. The guys that work on the chassis and the guy (me) that works on the aerodynamic surfaces. Namely wing, surface controls, tail and such. It is a standard pull configuration aircraft, tricycle landing gear. My problem here is that I am kind of undecided when it comes to my airfoil of choice, so I thought of giving the forum a go and see if anyone can illuminate or inspire me.

As of now, http://airfoiltools.com/airfoil/details?airfoil=naca643618-il has been my choice, but maybe I am starting to think that other options could be better so let me write here a few specifications that could come in handy regarding the aircraft.

The main body will be build of steel tubing covered either in Aluminium or fabric. This will be the final choice once we calculate how much lift we can actually produce.

The wings and other surfaces will be made out of carbon fiber. I will be the one mainly working on this, and they will be attached to long solid cuboids spanning from one tip of the first wing, through the body and all the way to the tip of the second wing. The shape and dimensions of these cuboids will be determined through a FEA after we have the correct wing profile (so we can play with the variables afterwards or maybe even find better solutions). The wings will either be attached with rivets to the cuboid or with standard well shaped bolts. TBD.

The aircraft is planned to be mostly used at not so great speeds. If we can achieve a takeoff at 16-20 m/s with flaps on it would be fantastic. I would not like the top speed to be anything great either. I mostly would use this in very good still weather to cruise around the fields. 

I can afford having an airfoil that is a bit thick, but would like to manage the turbulence that would be created by boundary layer separation in high thickness and/or camber foils. Maybe I will modify a bit my final selection. 

The wing will have flaps, in fact it will be a flap that extends at around 35% of the total span of the wing. It will be a modification of the slot and Fowler flap (a sort of optimized approach that mixes both) whose final geometry will of course be dependent on airfoil selection.

P.S : I use Fusion 360 for modeling, Autodesk CFD to calculate the total lift of the full 3D modeled wing/aircraft.
Terms fist, to avoid any misunderstandings:

What you call cuboids is normally called a wing spar. It consists of spar caps for the tension and compression loads and a web between the caps to transmit shear. And yes, it runs all the way from one wingtip to the other.

The spar carries the bending moment which has its maximum at the center and is zero at the tips (unless you use winglets). The more distance there is between the two spar caps, the lighter the spar can be built, so a thick mid-wing airfoil helps. Your choice of the NACA 64₃618 is a good start. I would advise, however, to taper the wing to something like a NACA 63₃412 at the tip. Thinner airfoils have lower minimum drag and higher maximum lift coefficients which helps to avoid the tip stalling first.

Or you move to newer airfoils which have been optimised for longer laminar boundary layer runs. Since you plan to use carbon/epoxy for the wings, you might take advantage of the exceptionally smooth surface this makes possible. The NASA contribution is of course the NLF series, NLF standing for natural laminar flow. The NLF(1)-0416 or the NLF(1)-0215 would be possible candidates. Even better designs might be possible when you search for modern glider airfoils; however, the published ones generally are at least 30 years old. Glider airfoils are optimised for minimum Reynolds numbers of around 1 million; when used in a GA aircraft this might be a bit conservative but could fit well to your low speed requirements.

The ultimate step could be to design your own airfoil. Take my glider recommendation and use XFOIL to tweak it to what you really need.

One last word on your choice of flaps:

When the inboard span uses powerful slotted flaps, their increased circulation will change airflow at the outer wing in such a way that the outer wing will stall before the inner wing had a chance to demonstrate it's lift potential. Either stay with plain flaps (for which the HQ-17 was designed - make sure you calculate it with a positive flap deflection at slow and negative at fast flight speed!) or add slats to the outer wing. In order to keep complexity manageable, I would recommend to use plain flaps and flaperons over the full span.