Are you soldering the chips directly or are you soldering breakout boards together. Those are very different problems.
If you are soldering breakout boards together, I’m not really sure of what advice to give you.
If you are dealing with the chips directly and the HM-10S/HM-10C as a castellated module, I think ExpressPCB will assemble boards for you for about $500 (presumably base–parts will probably need to be added).
I would use a 4-layer board (signal-GND-VDD-signal) unless you have an amazing reason not to–2-layer boards make your life miserable with routing, power distribution, and heat dissipation. The cost differential just isn’t worth it unless you are shipping 100,000 boards.
You might have a bit of an issue in that I can’t really seem to find a reliable/trustworthy supplier for the HM-10S/HM-10C castellated modules (Seeed has the HM-11s so they might work). That means you will have to buy the parts and ship them to the assembly house–that’s probably an extra charge.
In terms of designing boards, use KiCad. It’s more than adequate for what you are doing. It’s open source and sponsored by CERN who figured out they were paying so much to PCB board software houses that they could fund it themselves. It works on Windows, Linux, and OS X (maybe not the latest M1 Macs though). I use it for all my BeagleBone capes. There are lots of tutorials and videos all over the place about using it. I use more professional PCB software for work and let me tell you that KiCad is perfectly fine to do PCB work in.
I would suggest, however, that you switch to all SMT components if you’re going to use an assembly house. Through hole requires hand soldering operations (read: expensive) while SMT allows the assembly house to stencil the solder paste and then pick and place the parts in a fully automated fashion (they probably use humans for this on orders of 10 or less, but the expense of through hole still remains).
In terms of hand soldering, I oddly find that SMT SOIC packages and 1206/1210 SMT components are much easier to solder by hand than through hole packages and 1206/1210 components are large enough that I can solder them without a microscope even with my aging eyes. I will suggest that you need two soldering irons though. Soldering SMT passives like inductors/capacitors/resistors is dramatically easier if you can hit both terminals with heat simultaneously.
One thing to be cognizant of is that an assembly house will default to Pb-free solder. This requires quite a bit more heat to melt if you have to do hand rework. I find that I generally have to add leaded solder to the solder joints in order to bring down the melt temperature for hot air guns to work.
If you go all SMT, you have an extra option that you didn’t have before–you can stencil and reflow the boards yourself.
You need some solder paste. And you also need to buy an SMT stencil printer (as low as $60 on AliExpress–but I strongly recommend the $300-$500 range ones–the difference is in the number and accuracy of the vernier adjustments). And you need to buy some sort of “reflow oven”–that can be a cheap toaster oven depending upon what you need (note the one in the ATXHS electronics area) or you can get one of those from AliExpress (I think you can get those as low as $200) and there are lots of videos about how to use them for hobbyist work.
At that point, you can print the paste on the board with the stencil, place the components by hand, and run the board through your “reflow oven” to solder it. For SOIC and 1206/1210 components I find that setup works really well and I almost never get shorts. The stencil cuts back the amount amount of solder so you don’t oversolder the joints, and the surface tension of the solder gives you quite nice joints on the SOIC and prevents short circuits.
If you have a problem, generally it’s that a joint didn’t fully solder rather than shorted out. And that’s easy to spot under a microscope or magnifying glass as you’ll see little solder balls still intact. You need to hit that joint with your soldering iron or hot air gun and finish it off.
Hope this helps.