My usual approach to this sort of thing is to panel mount everything as much as possible. Preferably using switches etc that can be mounted in round holes, because drilling square holes is tedious and always looks a bit shonky, though is usually necessary for displays
[1]. The ubiquitous 16x2 LCDs are a good bet for panel mounting if it doesn't need to be waterproof. If you get the ones with an I
2C interface on the back, it's a neat 4-wire connection to your Arduino or whatever.
Otherwise, a case with a clear lid saves a lot of effort if you don't mind the electronics being on show (although masking out a window and spray-painting the inside can work okay
[2]). I've done the cut-a-hole-and-perspex thing a couple of times, and it
always looks like a bit of a bodge.
Top tip: If it's more than just a couple of power connections, use connectors between the panel mounted components and the board to aid serviceability. It's tempting to solder wires to the board directly, but you'll inevitably break one while fitting it all together, and now you're trying to work out where that loose wire goes without breaking another one.
If you're not interested in an electronics project, then the timer pointed to by grams would be a good bet. If it's not clear, that just slots into a rectangular hole and the tabs hold it in place, as is common for cheap panel meters. Works best if the panel is less than 3mm thick.
[1] Having tried various approaches, my preferred method for cutting square holes in ABS or aluminium is to drill accurately-placed 3mm holes to mark the corners, and join them up using either a Dremel with a grinding disc (flexible shaft helps keep things perpendicular) or by melting through the plastic with a nasty old soldering iron I keep for the purpose. Some filing will then be required to make things straight, but filing ABS isn't too tedious.
[2] One thing that works really well with LED displays is to use translucent red ABS, mask a window and spray the rest of the inside black. As no light can get through, it appears almost black, apart from the digits shining through. As a bonus, it greatly improves the readability compared to the bare LED display module.