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If you 'have' 25+ servers, I would hope that you wouldn't be 'new to backups' or indeed be confusing 'backup' and 'standby' in your mind.
A common method is to have exact duplicate hardware and software installed, and periodically copy across any live data so that when something fails, services can be pointed at the standby server.
This is unrelated to keeping security backups of any data involved, and one does not substitute for the other.
Then you're going to have to estimate the needs of the replacement servers, in terms of data storage space, memory, and CPU speed actually needed, plus any special features such as data feeds, specialised hardware or whatever. Not necessarily by just adding up what the current boxes have, but also adjusting by what fraction of the available resources are actually used on each existing box.
One possibility to ease your pain is to have the new machines on a couple of bigger virtualised boxes. That way if you underestimate one requirement a little and overestimate another, it'll all even out. A virtualised setup would make it easier to move the old 'machines' to new hardware as you find out what the real load and requirements are.
Linux, Windows, Solaris, and others, have a variety of virtualisation solutions, some of which you can play with ("evaluate") for no money while you get a feel for them. Why not spend a little time doing that?
Then you might make a copy of one existing machine's environment into your test virtual environment (being careful not to let it interact with your live system in any way) and see how easy/hard the migration process and management of the virtual system is.