Some of this sounds like a business decision to me. You'd want to send them to a page that best achieves your goal for visitors to that domain. In most cases, that would probably not be your home page.
So if you do a 301 (Permanent) redirect from your domains, if those domains have any backlinks, you will pass the link equity along to the redirect target page (i.e. the page on your site). The domains, if indexed, will be deindexed. Of course once the 301 is removed, they will be indexed again and any links pointing at the domain will no longer be treated as if they point to your site.
If you do a temporary (302) redirect, the domains will remain indexed (if they were to begin with) and you won't pass any link equity to the target page. Typically, 302's are used for things like a product that's temporarily out of stock on an ecommerce site. They used to be used for faking page rank, but since toolbar page rank hasn't been updated in months (and probably won't be updated in the future) there's little likelihood of them harming your domains in that respect.The drawback is that the indexed domains will have the content of the target page, so you will have duplicate content issues.
So 301 = cleaner for your primary site but deindexes the domains. 302 - preserves indexed domains and their link equity, but at the risk of weakening the target page through duplicate content.
I would definitely NOT 302 redirect a bunch of domains to your home page.
As for pointing the nameservers to your hosting account: Does your hosting plan let you "park" domains? If so, you could do that and park them. By default though, this will direct their traffic to your home page so the problem with this from an SEO standpoint is you'd have multiple domains with your home page content = duplicate content. A better way to do park them would be to use a script to read referrer info and send traffic for the domains to a different page (even a customized "for sale" page) than visitors to your site. So more work up-front to implement well from a technical standpoint.