While Classic Mode Difficulty restricts you to default abilities and stock weapons, you're still allowed to collect and use Locker Keys, capacity Pouches, and the Shooting Range to earn additional Gun Powder, Healing Herbs, and a couple more Keys. Since the Range normally gives Weapon Parts and Gel, the rewards are changed up.

If the limited saves and abilities are making you feel apprehensive, you'll have an excess of Gun Powder and Herbs to work with if you take the time to do some of the Range just before you make one of your 7 saves. While it is by no means necessary, it's an option should you decide to use it.

Here is a comparison of the Shooting Range's Classic Mode specific rewards and the original reward list.

You're allowed to use any pistol or weapon at the Range, even a shotgun or the assault rifle. However both Chain Attack and the normal Gallery reward precise shots, so it's recommended to stick with a pistol. Even though you're timed, you will have enough time to line up most of your shots.

The zoom level does differ slightly between each pistol when you aim, so pick one you're comfortable with. In Classic, you're likely not going to bother with most weapon variants; you just want to get it done and put as little time in-between saves as possible while making the most story progress.

These were taken with FOV set to 80.

Your default trusty pistol. You literally can't leave (someone else's) home without it!

The Laser-Sighted Pistol is an easy variant to get in Classic. It's gotten off a corpse in Chapter 3 at the Union Auto Repair lot. Make sure to mash 'A' and 'D' as you get it, as you'll be grabbed in a cutscene.
Note the significantly increased zoom, which I found a bit much for Chain Attack. The laser is nice, but you lose your crosshair.

Feel like a cold professional assassinating squares with this Silenced Pistol. It is given to you by Sykes after his first sidequest involving turning the server power back on, allowing him to open the cache in his Safe House (and others) for you.

Sebastian's original revolver from the Beacon Incident. Given to Seb after he comes to terms with his trauma from the first game and defeats the Anima. Slightly more damaging at the cost of accuracy; not ideal for the Gallery as almost every target takes one shot.

The strongest handcannon this side of Union. Not obtainable in Classic, but including it for completion.

The Shooting Gallery and Chain Attack will be open for play once you reach Chapter 4. It won't show up immediately if it's your first time returning to your office after the introductory chapter. You need to sit in the upgrade chair first, then exit your office and come right back. The door should appear at that point.

Completing the Gallery mode awards a key, 52 Herbs, and 40 Gun Powder. Completing most of the Chain Attack mode awards another key, 44 Herbs, 24 Gun Powder, with an additional 100 Powder alone if you reach the final tier. Then go out there and kick those Lost in the face!