Water Sprayer

Used to dampen garments when they're too dry. Often also used on Cotton to get a better - crisper - finish.

Teflon Iron Shoe

An accessory that can help reduce shine, give a smoother ironing action  and increase the heat setting for any material type. Some kind of shoe is normally available for any iron.

Not only can you reduce shine but you can often increase the temperature of the iron on any cloth using a shoe (you should do this only after you have some experience using the shoe).

Ironing Board

You can iron on any solid surface that has a covering on it, a table, a board or even a rolling pin for those hard to get to areas.

However, normally a board will be shaped, be covered with something that has some of padding under it and have a variable height. That ensures you can easily move a garment around the board and yourself around the garment.

Lint Free Cloths

These are used damp and on top of garments that may shine. Some fabrics are very susceptable to shining due to direct heat, or may even stick to the iron because of softening due to heat. 

You should particularly be wary of woolen suits, which shine very readily.

Either use the water spray to dampen or place the cloth under a tap, dampen well and then wring out before using on the garment.

Flat Iron

From travel irons to professional options with boilers all will do a good job if you follow the basic rules.

Your choice of iron will depend on your usage. doing a family load of ironing with a travel iron can be tedious and long, whereas heating up an iron with boiler to iron a handkerchief may be overkill.

Steam irons are the norm nowerdays but you may get a better job done by using a normal flat iron and the water sprayer described above.