Hello, and welcome!
Your stitches look very nice, and you are right about the size of the holes in relation to the size of the thread. Those Tandy 4 in 1 awls are good for the birds as far as stitching goes. You would be much better off buying yourself one of those C.S.Osborne diamond point awls, IMO. You can find them on the Tandy (and others) website. These make much smaller holes than the Tandy 4 in 1 awls, and your stitching will look neater.
Frankly, that prewaxed linen thread that Tandy sells is not very nice thread. It might do in a pinch for large projects, or to tether your dog, but it is much too heavy for smaller items such as wallets and checkbooks, etc.
As far as thread goes, Royalwood sells prewaxed linen thread in many colors and several sizes. They sell a sample card for $2 that gives you samples of the different size threads and the different colors so you can judge for yourself which size is suitable for your project.
The only problem I find with prewaxed thread is that there is always way too much wax on the thread. You can fix this by folding a piece of heavy brown paper over the thread and rubbing back and forth very briskly. This melts the wax further into the thread and removes excess at the same time. Makes the thread much easier to work with.
Also, don't get sticker shock when looking at linen threads. It's quite expensive. A #1 spool Barbours unwaxed linen thread costs more than $40, so the smaller spools that Royalwood sells can be a good alternative, especially if you want different colors.
As to thread size comparisons, Barbours 5 cord is roughly 1/2 the diameter of Tandy's waxed linen thread. This size is great for smaller items. For larger items, use a larger size such as 7 or 8.
Now I'm going to let someone else here jump in and offer advice on needle sizes, and where to get them.... I hardly ever hand stitch any more, as I'm spoiled beyone belief with 2 nice stitching machines.
Good luck, and have fun.