Before you power up the machine there are a couple of things you should check.

First open the back box, remove the back glass, and inpsect the main MPU board. this is the big board on the left side. In it's stock configuration, there should be a battery holder on the MPU board with three AA batteries in it. Most folks move these batteries off the MPU board into a remote battery holder. The reason is if the batteries start to leak, the alcali can do some serious damage to both the MPU board the driver board mounted under it. if the batteries are still on the MPU board, and they have leaked STOP here. Chances are the machine won't boot, and you are going to either get the boards repaired or replaced.

If the batteries are all good then verify all the fuses are the proper amperage, and none of them are blown. When you check the fuses, use a volt meter to verify you have continuity through the fuse, you can't depend on a visual inspection. Ive seen people try to substitute higher amperage fuses than the system is designed to use, and this can lead to very bad news if something goes wrong.

The fuses are as follows:

On the power supply from top to bottom:
F1 - HV .25A Slow Blow score Display
F3 - Lamp matrix - 8A Fast blow
F4 - Not used in Laser Cue
F2 - Solenoid 2.5 A Slow Blow
F5 and F6 Logic Power - 7A Slow Blow

The flipper board down below has a 5A slow blow fuse.

There are also 4 - 5 amp slow blow fuses on the side of backbox that are for the general illumination (GI).

If the fuses are all good, you are ready to try to power it up. If the games boots, chances are it will come up in audit mode (you will see a four or five digit number in the player 1 display, and no other controlled lights will come on). To get it out of audit mode and into game over mode, open the coin door, and quickly turn the machine off and on again. This should make the machine go into attract mode, and the controlled lights should start blinking.

Good Luck!

Before powering up, best practice on an unknown game is :
test all coils in the game for correct resistance and verify no shorted coils.

https://www.pinwiki.com/wiki/index.php?title=Post-Purchase_Checklist

Congrats on your new purchase, the first one is always exciting.

-For games that are new to me I like to visually inspect the machine top to bottom and look for anything broken, loose or out of the ordinary taking notes as necessary.
-Verify with your multimeter that no coil under the playfield is testing lower than 2ohms or higher than ~50ohm.
-I verify all fuses that are in the machine are the proper ones.
-I isolate the power supply by unplugging everything that it feeds. I only leave in the connector(s) that give the power supply power from the transformer.
-I power the game on and verify I'm getting all the proper voltages on the test points of the power supply. If I'm not I may either wait until I've resolved the issue(s) or pop out the fuses associated with the wonky voltages and see what the game will do with it only partially powered.
-Once I've done all that, I feel confident enough to turn the machine on for real with my finger on the power switch in case anything starts smoking.

It's counterproductive to power the game on without an inspection because if you blow something you'll spend more time and money than you could have. I also like to keep things as original as possible so I keep in mind that I don't want to destroy something working that's original just because I was impatient. Don't be afraid to make mistakes though, it's the only way you'll learn.

To a new pinball person nothing looks ordinary.
I second ForceFlow ’s Pinwiki link.

My 1st big project was Alien Poker.
I sent all the boards out for flat rate repair.
Had a new flipper switches installed. The right was a pain.
Thingaverse had a file for the drop target spacers. I found the targets came out warped as they cooled unevenly.
Otherwise, should be all about the playfield inserts and wear on the initial launch path.
LED's were easy BUT you have to get all the bulbs out. I had a few stuck and it looked crazy until I got them all swapped out.
Usually the displays gas out. Buy a new kit.

I always inspect all fuses for rating, still good and fuse clip strength and tarnish.
I inspect the coils visually and by manually activating them to make sure they have free movement. A burned coil is a clue that some board work may be needed. I also tug on the coil diodes while I am there.
I then inspect the boards looking for burned components (the lamp resistors are usually toasty but not necessarily bad). I tug on the socketed chips by hand. If 1 comes out that socket needs to be replaced.

When you turn the machine on listen for activated coils (ignore the coin reject coil in the door). Turn off immediately if a coil locks on or you smell burning or hear buzzing.

Take the backglass out, wrap it neatly and store it somewhere safe. You wont need it again until your game is up and running and only bad things can happen if you keep removing and reinstalling it as you work.

Read the links people send you. Then reread again. No shame in asking questions if you dont understand parts of Pinwiki but the more you try to figure out on your own the better you will understand the answers people give you.

Obv check fuses before powering on

Post pics! Questions with pictures always seem to get more thorugh replies. You will be amazed what issues Pinsiders can identify will just a photo

Work methodically. Visually inspect connections, boards looking for anything unusual and post a picture if unsure.

Looks nice! Here's the Pinwiki page on Sys 3-7 games: https://www.pinwiki.com/wiki/index.php?title=Williams_System_3_-_7
I would also keep in mind which fuses on there right now are blown (assuming they're rated correctly), as this might give you a hint to potential problems the machine has.

Not a good idea. If you happen to only have a 2a for a part that requires a 2.5a that would be okay (still not preferable, I only do this temporarily if I don't have the proper fuse on hand), but I wouldn't ever go over the rated amperage.

If you're not too familiar with soldering I would suggest practicing on a scrap electronics board first. I would recommend a Hakko FX888D iron, and a soldapult (or a Hakko FR-301 desoldering gun if you can afford it/are going to be doing a lot of repairs). I use Kester 60/40 solder, and source parts from GPE, Arcadepartsandrepair, Marcos, PBR, Digikey and Mouser. I learned a lot by watching Joe's Classic Video Games on Youtube, as well as reading Pinside.

Fuses are chosen based on the equipment they are protecting. If you use a fuse that allows more current than the circuit is designed for the fuse may not blow before the circuit components are damaged.

Pinball Life carries the fuses you’re likely to need. Get a few of every size in the machine.

Good idea to make a circuit breaker if you’re doing a lot of troubleshooting. http://www.pinrepair.com/em/index1.htm#tools
Read the circuit breaker section if you make one. Your ss game uses fuses with lower amperage rating, as described in the article.