Grands use the larger rubber muting wedges and uprights require the smaller ones with wire handles. Four wedges of each type will suffice. You can buy these by mail order or you can ask your tuner to buy the whole set of things you need for you.
The most popular muting strips are felt, about 4 ft long, 5/8 inch wide. They are used to mute out the two side strings of the 3-string notes in the octave used to "set the bearings" (see below). They also come as ganged rubber wedges but these don't work as well. The strips also come in rubber, but rubber does not mute as well and is not as stable as felt (they can move or pop out while tuning). The disadvantage of the felt strip is that it will leave a layer of felt fiber on the soundboard after you are finished, which will need to be vacuumed out.
A high quality tuning lever consists of an extendable handle, a head that attaches to the tip of the handle, and an interchangeable socket that screws into the head. It is a good idea to have a piano tuning pin which you can insert into the socket using a vise grip so that you can screw the socket into the head firmly. Otherwise, if you grab on the socket with the vise grip, you can scratch it up. If the socket is not firmly in the head, it will come off during tuning. Most pianos require a #2 socket, unless your piano has been re-strung using larger tuning pins. The standard head is a 5 degree head. This "5 degree" is the angle between the socket axis and the handle. Both the heads and sockets come in various lengths, but "standard" or "medium" length will do.
Get two tuning forks, A440 and C523.3 of good quality. Develop a good habit of holding them at the narrow neck of the handle so that your fingers do not interfere with their vibrations. Tap the tip of the fork firmly against a muscular part of your knee and test the sustain. It should be clearly audible for 10 to 20 seconds when placed close to your ear. The best way to hear the fork is to place the tip of the handle against the triangular cartilage (ear lobe) that sticks out towards the middle of your ear hole. You can adjust the loudness of the fork by pressing the ear lobe in or out using the end of the fork. Do not use whistles; they are too inaccurate.
Ear muffs are a necessary protection device, since ear damage is a tuner's occupational hazard. It is necessary to hit the keys hard (pound the keys -- to use a tuners' jargon) in order to tune properly as explained below, and the sound intensity from such pounding can easily damage the ear, resulting in hearing loss and tinnitus.