Can I customize my 2005 apple mac mini with Cinema display monitor or would it even be worth my time?

While my old Late 2005 Mac mini G4 1.5GHz runs Mac OS X 10.5.8

..and can use TenFourFox when that's updated to work by maker..

it also has and can still use, an Apple Cinema 20-inch display.

Other vintage displays also work, some with an extra adapter.

This Display was introduced as lower of a series told of here:

• Apple Cinema Display (20-, 23-, and 30-inch DVI) - Technical Specifications

https://support.apple.com/kb/SP79

Not sure that I understand the context of your inquiry.

Explain "customize". At the moment, Late 2005 Mini

has Samsung 19-in Dual-hinge flat panel that rotates.

A newer mac build year model, of Intel-based Mac

hardware or maybe M1 Apple Silicon, is an upgrade.

The older PowerPC Mac series hasn't a recent model

since the Late 2005 build year; as my Mac mini G4.

Because hardware and software have done leaps of

improvement and air-miles of change; new(er) ones

needed. There's no new software made for old Macs.

Sources of newer refurbished Apple Macs, include

online Apple Refurbished store. Also some reputable

resellers or AASP who may have restored models, may

less cost than retail/new price. The Apple Store online

has latest build models, at retail, with original warranty.

Options include Apple Care+ extended plan coverage.

An upgrade can mean to get a replacement; if no path

forward to Current, or 'less vintage', exists from old state.

The hardware upgrade follows newer system software.

Newer systems are downloaded from Apple servers.

• How to get old versions of macOS - Apple Support

https://support.apple.com/en-us/HT211683

..To get newer hardware would expand your capabilities..

Good luck & happy trails!

🌞🌿⛵️🎣🌻🐢⛄️🌤🌎

There are no dumb questions. Some of my replies are not equal though.

Links in 'old software' added above ~ have ingrained ideas on upgrades.