The online resources I’ve read suggest this will allow me to use
different plugins and themes on the two sites whilst allowing a search
from either site to bring up results from both sites.Is this correct?
Yes, is correct. In multisite environment you can install different plugins/themes for different sites.
Once the database is the same, you will be able to do cross-site searches, but there is no built-in functionality for that, you can built your own or use one of the plugin that bring that functionality.
If I set-up a multisite, is it possible/straightforward to keep the
main site at www.domain.com whilst having the ‘info’ site remain
accessible via ‘info.domain.com’?
Yes is possible. Easiest way is to use a mapping plugin that require some server setup. Look at this.
Is there a better solution?
I don’t think so. Another possible solution is make the database of the 2 installs mutual accessible (every install can access the db of the other install), then write some custom code to merge search results from a site with results from other.
Believe me, it’s not so easy, because handling permalink structure, custom rewrite rules, cpt permalink… easily becomes a pain. Also consider that in this case you need a second database connection, so you’ll have lower performant searches.
Multisite solution need that you move your content form single installs to a multisite install, but is not a rare task, and it should be relatively easy and you can find some help searching web.
Consider that multisite brings other features, like share users, and then you need to mantain and keep update only one install instead of two.
A possible downside is that being on same server the 2 sites will share the IP and maybe it can have some effects on SEO (I’m not a SEO expert, maybe ask one).