Here's my new and first SS.
It's also the first new bike I've ordered online and put it together myself. I don't have a torque wrench or any fancy tools. Is there anything I need to be careful of or have a shop look over? Especially since I am a novice putter-togetherer. I have taking it out for only about 10-15 miles so far.

It seems all pretty straightforward, but I don't know if I might be missing something.

From my recent experience:

Grease everything with threads, look up info on exactly what to grease.
Lube certain things like your chain. Also check your chain tension.

Might have to install/tighten your pedals, should be done with a pedal wrench.

Get your wheels looked at, see if they spin true.

Some of these should be done before seriously riding.

If you don't have a torque wrench I'd recommend having the bike shop at least double check if your cranks are tight enough. They can be damaged if they're not torqued down enough. Also, make sure your headset is tightened properly. I'm not an expert on this and maybe someone else can chime in on the steps for this.

It is pretty straight forward but there are specialized tools for things like the bottom bracket, hub cones, and spoke nipples. You can't work on those parts without the special tools. You can go to a shop to have them look it over but they may charge. They most likely will charge to look over the BB because there is more labor involved.

+1 on the headset. Make sure the top cap is pushing the stem and not the steer tube

You don't need a torque wrench if you have common sense and a general understanding of the material properties of the components you are workign with. I've never bothered with a torque wrench, not even with carbon, and have never f'ed anything up.

Pick your bike off the ground and drop it...does it sound solid when it bounces or does it rattle? It it rattles, something needs adjustment. If the threads are greased, everything spins smoothly, the wheels stay true and nothing is loose, and, your bike stays in that condition mile after mile, then its more or less assembled correctly.