Advice for swapping out the gas dryer theself

My (rather old) washer blew up on me a few weeks ago (Apparently it's been unbalanced for a while. Came with the place and I never thought too much of the vibration until it was too late.) and am getting a brand new set delivered on my new set (Washer HERE, GAS Dryer HERE) from Sears on Thursday.

They wanted about $80 plus parts to install them (I forget if it was each or for both) and I declined having just disconnected everything myself, I figured it would be easy enough to set up the new ones. I'm not particularly handy but I'm at about replace-my-own-ceiling-fan, remove-and-reinstall-my-own-garbage-disposal level.

I'm not overly concerned about the washer, but I was reviewing the manual for the dryer online and it's got me a little nervous. It talks about needing to purge the gas line of air twice, using teflon tape (I didn't see any evidence of that on the old install), etc.

So I wanted to pose the question- is this something that someone at my level can handle myself or are there enough gotchas that I should cough up the money?

EDIT: I succeeded today thanks in large part to the answer here- thank you.

I wound up buying 'yellow' gas-approved teflon tape and a new flexible gas line (to be safe… It was $30 though!). And a new dryer vent hose (also pricey) since apparently I needed a metal one and the existing one was foil.

It was about as easy as I hoped.

To recap:

1. I connected the (new) exhaust vent hose using the pressure coupling rings (not sure the correct term) that came with it on both sides- wall and appliance. The manual demanded not to use a foil vent, so I used a metal one. (Unfortunately, the most flexible metal one I found pushes the dryer out too far from the wall for my needs- I can't close the door to my laundry cabinet now!… Subject of another post I guess. I'm going to try a "periscope" dryer vent.)
2. I connected the new gas line to the valve on the wall, using a layer of yellow teflon tape on the threads (although the Home Depot guy seemed to think I'd only need it on the appliance side)
3. I connected one of the removable couplings from the gas line to the back of the dryer (again, used tape even though perhaps not necessary)
4. Turned on the gas for a moment to purge the line
5. Loosely threaded the gas line into this coupling, also using tape as recommended; purged again
6. Tightened with a (newly purchased) pipe wrench.
7. Turned on the gas and listened & smelled for gas at both connections – silent and odorless 🙂

Took maybe 30 minutes, most of that time was spent wrestling the pressure couplings and trying to get the threads to take- was trying to be very gentle.

Dryer started right up no problems and it (and we!) survived two test loads.

So, went well, I found it relatively easy and would do it again. Thanks for helping me build my skillset!

(Adding the requested photo here although it's a bit late. Note that I covered the hard-gas-line's opening with painter's tape and stuck it on/around the valve so you can't see it, but it's there. Wanted to protect it from all the lint and dust floating around down there.)