Hiya and welcome
A2000 isn't a very popular model and as you're after a gaming machine it makes even less sense for you.
If you're after games on the real-deal, you've really got two choices. You either go for an A500 and play OCS/ECS games or you go for an expanded A1200 and play WHDLOAD OCS/ECS/AGA games.
For the monitor choice, you either go really old-school and muck about with an old CRT or you go with an Indivision and use a modern LCD monitor. Another option is to go RGB to SCART to a modern TV (personally I'd recommend the Indivision option).
This will give you an idea how sharp an LCD can look with an Indivision ->
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So the cheapest way would be a pretty standard A500 with (for example) a floppy drive emulator or an A1200 with a RAM card and CF hard drive.
If you've got more money to burn you'd look at upgrading with an Indivision and maybe adding an accelerator card.
The only thing you'll miss out on is support for RTG games but there aren't really that many to be fussed about.