Of the changes that can be made to a room in an afternoon, replacing the ceiling fitting changes the most. Builders and landlords fit the cheapest available option, which is usually a bare fitting or a small drum, and it sets the character of the ceiling and the quality of the light for everyone who lives there afterwards. Replacing it is worth doing early rather than last.
It is also the project on this site where the boundary matters most, so it is worth stating plainly. Exchanging one fitting for another on existing wiring is routine. Moving the position of a light, adding a fitting where there was none, changing what switches control, altering anything in the ceiling void, or working on a circuit you are unsure about is work for a qualified electrician, and in many places is legally required to be. If the existing wiring looks old, if there are more cables in the rose than you expected, or if anything is unclear when you open it up, that is the point to stop and call someone.
Before buying anything, look at what the ceiling can carry. Many ceiling roses are fixed to a single joist or, worse, to plasterboard alone, and a substantial glass or metal shade weighs far more than the fitting it replaces. If the new fitting is heavy, the fixing has to be into timber, and that may mean the fitting needs to be positioned slightly differently or the ceiling opened to add a batten, which again moves the job into someone else's hands.
Then deal with the drop, which is where most fittings disappoint. Over a dining table, hang the fitting so that the bottom sits roughly seventy-five to eighty-five centimetres above the table. In an open space where people walk underneath, the underside wants to be at least two metres up. In a room with a low ceiling, a close fitting or a semi-flush shade will usually do more good than a pendant, because a pendant in a low room simply puts an obstacle in the middle of the air.
The shape of the shade decides what kind of light you get, and it is easier to think about than it sounds. A shade that is open at the bottom and closed at the top throws light downward, giving a bright pool and a dim ceiling, which suits a table and does not suit a room you want evenly lit. A shade open at both ends throws light up and down and lifts the whole room. A fabric drum glows and spreads light softly in every direction. A solid metal cone gives a hard-edged pool and dramatic shadows.
Give equal thought to the lamp inside, because the fitting cannot fix a bad one. Warm light in living rooms and bedrooms, neutral in kitchens and working spaces, and a consistent temperature across all the fittings in one room, since two different temperatures in the same space is instantly noticeable and slightly unsettling. If the fitting takes an exposed lamp, the lamp is part of the design and should be chosen accordingly.
One last consideration that is usually thought of too late: whether the light is on a dimmer, and whether the lamps you are buying will dim. A single overhead fitting at full brightness is an unkind light in an evening room, and the ability to take it down to a third does more for the atmosphere of a space than almost any other single switch. If the circuit is not dimmable, that too is a conversation with an electrician, and it is worth having at the same time as the fitting is changed rather than a year later.