Well, I'm not sure how they handle it now, because it's been a long time since I did it, but there was a "technicality" (for lack of a better word) about how home page redirects to inner pages were handled for quite a while and the old home page would show in the SERPs with the content from the page it was redirected to. (Much like an old 302 hijack even for a 301 redirect.)
So, that's something to keep in mind.
Also, I'm not totally sure about redirecting an entire site to a single page in any situation, unless the site being redirected was something like 10 pages and the topic of the page being redirected to was relevant to the pages being redirected.
If I was going to redirect I'd try to go the the most relevant pages as much as possible, page-to-corresponding-page would be my first choice.
If not, second would be to redirect a section of the old domain to a corresponding index page on the new one, so for example if old-example.com had a /fruits/ directory I'd try to redirect all the pages within /fruits/ to at least new-example.com/food/fruits/whatever-the-fruits-index-page-is.ext.
If I couldn't do those and it was very many pages I'd probably do the following.
Option 3: Not redirect at all.
I might noindex, put a notice for visitors with a link to the location I would normally redirect to if I was going to redirect and 10 to 15 sec meta refresh to the new location but I'm not sure on that, just an alternate "something" I'd consider in the situation. I would definitely use it rather than redirecting something like 1000 pages to a single page on a different domain though.