first things first ?

Some do, some don’t. Personally, since you already ordered the Vortek, I would: Run a patch, tighten (or check) screws. Scope it, shoot it as is. Check out some YouTube vids on how to take it appart, you may need something to compress the rifle a bit, I think most HWs need it. Then do the whole thing after you receive the Vortek. Don’t be afraid to do it, it’s really not that bad, just take your time. The Vortek on that gun should just drop right in. I clean all the excess goo, and lightly grease afterwards. You may get a couple shots that diesel after, that’s normal. 

*Get you some Ballistol for cleaning. 

I normally take a brass brush, dab a good amount of JB Non-Embedding Bore Paste on it, run it thru the bore about twenty times up and back. If I can't get to the breech, I don't get sweaty about it, I run it thru the muzzle...using due caution and care of course. There will be those who will poo poo this, but all my life I've been running rods thru the muzzles of steel barreled firearms with no problems, I don't see where a steel barreled air rifle is any different. Then I'll run patches thru the barrel soaked with Hoppe's #9...same philosophy, doesn't hurt steel barreled firearms, shouldn't hurt a steel barreled air arm...until I'm satisfied. Dry patches after that until they come out more or less clean. I'll wipe down the entire rifle with Ballistol, oil the moving parts I can get to with whatever lubricant suits me at the time...NEVER WD40 though...I'll torque the scope and stock screws. Then I'll have at. 

OP, what you'll end up doing is taking all the information that's out there, sifting thru it, using what makes sense and what doesn't. My method is NOT the end all to beat all, it's just what works for me! If you are uncomfortable with cleaning from the muzzle, don't do it! Use another method! If what you've read gives you concern about using Hoppe's #9, don't! I personally don't use any old cleaning rod that's out there, I've invested in Dewey coated rods. Only about thirty bux or less per caliber, they are cheap enough. 

My personal opinion is to shoot your new rifle for a while before you starting thinking about hot rodding it or tuning it. It might not need it, given what you want to do with it. For me, shooting an air rifle in my back yard is simply a release, a way to reduce tension and stress. Nothing more. My rifles don't need to shoot 15 FPS faster than stock, although I do chase the elusive ten rounds in a .22 caliber hole! 

Hi ya old fart. I'm kinda new to all these different brands and series.I've always had a couple of low grade springers, break barrel and underlevers.So which is the HW79? I looked at AGD, PA, and AoA but I did'nt see that model. I pretty much have always done as Yarddog has exccept I use a nylon bore brush and bore mops and q-tips. Anymore I just use straight up Ballistol. I've used 3 in1 oil but I have some sewing machine oil,(probably the same thing)I use on the trigger and cocking arm linkage.Now Tom Gaylord ,(Godfather of the airgun world) he's forgotten more about airguns than I will ever know, says to always use 100% silicon oil and grease for all the new airguns in areas of the breach,breach seal and spring,spring piston,spring piston cup, now because regular oil will degrade the nylon,delrin seals and o-rings that make up these power-plants now. Might get ya some Blue Lock-Tite for all the stock screws including the trigger guard. I recently ordered a barrel cleaning kit called ,The Patchworm Kit. Steve from AEAC uses these.He has an episode on ytube about it.They're a pull thru system,multible calibers. Sometimes it's quite hard to pull a brush back thru if it has'nt completely made it thru the bore.examples being under-levers and pcp's so to avoid possibly damaging the rod,brush, bore, or crown, I'm going this route myself. Hope this has been helpful, good luck

Nice choice! I’m looking to get one of those sometime this year I hope. 

Ah,,I see,nice,thx. What caliber did you get?

Welll...

The one time I tried using a rod and brush from the muzzle I nicked up the crown even with the nylon cone. I didn't have enough hands to hold everything in place and the cone slid, letting the rod damage the crown. I still cringe thinking about it! If I'd had a gun vise I would probably have been OK, but from now on I use some sort of pull-through loop cleaner like the Crown Saver Mac1 sells. 

If your gun has the beech stock, be cautious about over tightening the stock screws, just tight is good. Here's an article from another forum about hardening the screw hole area of a wood stock using superglue.

https://airgunwarriors.com/airgun-talk/how-to-treat-your-stock-and-lock-tite-stock-screws-for-better-springer-accuracy-an-easy-but-new-tutorial/

I haven't tried this yet, but I plan on doing this with my next springer. I have had issues from over tightening stock screws, the worst of which was a broken screw on a BSA springer which the previous owner must have overtightened in the past-almost had to scrap the gun but finally got the screw out with an extractor after about four tries-not fun!

Just checked out that link provided John. That is a really good article and tip.I'm gonna apply that to my springers,Thx John