Perhaps more important than the size of the screws (or other fasteners) is what they actually grasp. With any significant load, a screw will not hold by itself in tile or plaster. The tile will chip and the plaster will crumble.

One possibility is to use an anchor through the tile and plaster that expands laterally. There are several types (plastic, metal, etc.), but these are also generally used for lighter loads that are close to the wall, not a shelf that sits on brackets that act like levers, tending to pull them through the wall:

If your plaster is attached directly to masonry, there is an expanding anchor that is meant for that:

It must be placed in the masonry, not the plaster.

If there is a hollow space behind the plaster, a third type of anchor that mushrooms behind the surface could be used:

A fourth kind is a toggle that is inserted folded, but then opens behind the surface of the plaster and its fastening:

If the wall behind the plaster is hollow, this may be the best type of fastener.

If there are studs behind the plaster, the strongest fastening is to align the brackets with the studs and go through both the backsplash, plaster and finally into the studs with wood screws (wooden studs) or screws designed for metal studs.

Wrenches

Pipe Wrench

You'll want at least 2 of these, of different sizes.

Tongue-and-groove pliers

These come in handy all the time, have a few pair at the ready at all times.

Strap/Chain Wrench

Sometimes you just need to get a good grip on a pipe, nothing beats a strap/chain wrench fo this.

Basin Wrench

For those hard to reach places.

Adjustable Spanner

A few adjustable wrenches of various sizes always come in handy.

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Tape Measure

You're going to have to measure something, eventually.

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Pipe cutters

Copper pipe cutter

Pex/Plastic tubing cutter

Hacksaw

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Pipe reamer

You can get ones that do both inside and outside reaming in a single tool. You'l also want a bit of sandpaper.

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Pipe Cleaner

Used to clean up the ends of copper pipe before soldering.

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Taps and Dies

You might find yourself in a situation where you have to thread some pipe yourself. For this you'll need some Dies, and possiply taps.

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Torch

Working with copper is likely going to require some soldering, so you'll need a good torch. DIYers usually grab propane, or butane torches. If you've got the extra cash and you'll be doing a bunch of soldering, MAPP torches are what the pros use.

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Hammer

Do enough plumbing, and you're going to want to pound something into submission at some point.

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Putty knives

You'll need this to scrape gunk off of stuff.

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Auger

A great tool for clearing gunked up drains. Either manual or powered, the choice is yours.

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Glues, Puttys, and other gunk

PVC primer and cement

You'll need this if you're doing any work with PVC.

Dope and PTFE tape

If you find yourself working with threaded connections, you'll want to have some pipe dope and PTFE tape.

Solder and Flux

When working with copper, you'll probably have to sweat some joints.

Penetrating oil

Great for those really stuck joints.

Plumbers putty

You'll need this if you're installing sinks, and/or faucets.

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Buckets

You'll always want to have a couple buckets of various sizes on hand.

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A Box

The more jobs you do, the more left over fittings and other bits & bobs you'll have. The longer you do plumbing work, the larger the box will have to be.

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Gloves

Leathers

You'll want a good pair of leather gloves, for when you're soldering and doing other knuckle busting types of work.

Rubbers

You'll also want some rubber gloves, for when you've got to touch stuff you'd rather not touch.

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Plumbers Crack

You can't call yourself a plumber, unless your crack is hanging out. It's also great for warding off people who have "just a quick question", or want to offer "advice".