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The biggest hurdle is replacing 3rd party addons - from memory relatively few have upgrades all the way, it depends what the site uses. Others may require extensive workarounds (the “Gypsy” field type for EE1 springs to mind).
So the first step is to find out what 3rd party addons the site uses then either:
There’s always the option to do a full rebuild so you can take advantages of the many new features that EE6 brings, you should be able to import most existing content using a data import addon, plus it gives you a chance to dump the old bits and start afresh. Sometimes a rebuild is a whole lot less hassle than an big upgrade.
As Rob said, your biggest issue will be finding compatible add-ons if the site relies on them since most old add-ons don’t work anymore. Even official ones don’t work anymore, example, the Wiki module does not work on the latest EE 6 release. Not yet at least.
That version 1 is so old you will probably have to rewrite most of the code but is not only true for EE but any CMS, if you did not upgrade for years, you will in most cases just rebuild things to the new software using the same content.