How many links (internal) is too many?
Here is a visualization of the number of links on the homepages of top 98 webpages. Very few have less than 100, and many have 500 or more.
Google used to recommend that any page have no more than 100 links per page. However, they removed the "100 links per page" from the webmaster guidelines some time ago. Matt Cutts released a video where he says that the limits for page size and number of links per page are much higher than they used to be.
I've personally worked on a website with 250-400 links on every page. That site did very well in search engines.
I'm not sure what the upper limit today actually is. I'd keep it at no more than 500 if I were you. Above that and I'd think your site would be an outlier compared to other websites.
Unrelated to the number of links per page, your website about IP addresses is likely going to have other ranking problems if you have a page for every IP address. That is a lot of pages and most of them are not going to have much content. You probably only want to submit the pages with the most content to search engines.
I remember that Google was trying to remove phone number sites from its index a few years ago. Partly that was because so many of them had "Be the first to say something about this phone number" style blank pages.
Ideal would probably be 50. 100 works too if you want to go on the higher side.
Taking your points one at a time:
UX: Unless I misunderstood how this website is to be used, a search feature would be much more useful than a list of IP addresses. That way, people can look up the domain or IP of any websites that they have had issues with. However, maybe if someone is simply looking for spam IP addresses, this could be useful to them. In that case, it may be more advantageous to simply have a page listing the IP addresses and domains in a table with different "pages" for each category (hack attempts, spammers, and stealth bots). That page could be linked to instead. If you still wanted to stick with the links on the bottom, I would say random works best since seeing only a small, static section every time when visiting the site becomes old. If you were to take the random approach, a maximum of 50 would be needed I would say.
Download Speed: I honestly doubt having 50-100 links on a page would affect it barely at all...
Google: As with everything, Google seems to answer that it should be optimized for users more than for search engines. They also say that 100 is suggested, but it is not a hard limit. Matt Cutts even says himself that:
These days, Google will index more than 100K of a page, but there’s still a good reason to recommend keeping to under a hundred links or so: the user experience. If you’re showing well over 100 links per page, you could be overwhelming your users and giving them a bad experience. A page might look good to you until you put on your “user hat” and see what it looks like to a new visitor.