What kind of hardware/software config should I look at for a MySQL database with 10,000 plus tables
welcome to the dba.StackExchange.com website, and it looks like you've got quite a pickle. So before I answer the question that you posed, I'll mention some details to (hopefully) get you off to a good start:

10,000 tables in a database are always wrong.

I take that back. If you had all of the Microsoft or IBM corporate databases on one server, 10k tables might be appropriate. However, the data aggregate that outlines is enormous. So we'll overlook the "it's possible to be right" and stick with the 99% of statistical non-outliers. For all intents and purposes if you suggest 10,000 tables to a dba, they will laugh at you.

I'm going to hazard a guess that your tables look like: (I don't mean the exact structure, I mean the concept of the structure)

website1_articles
website1_navigation
website1_overhead
website1_blogs
website2_articles
website2_navigation
website2_overhead
website2_blogs
.......
website375_articles
website375_navigation
website375_overhead
website375_blogs


which would (for this very simplistic example) yield me right at 1500 tables. But if you'll notice, the only thing that changes on each one is the website ID.

I could instead normalize to include a website ID on each record and reduce the entire mess to four tables.



Now, I know what you're thinking: 


  "But that means I have to redo my entire database architecture, and it will ruin everything."


OR you're thinking:


  "But that will destroy the security, because then anyone could read anyone else's website information"


But really a) you've already killed the database by suggesting 10k tables, and b) this is in no way different than what you're suggesting.



Of course, it's entirely possible I'm wrong here, but anytime anyone suggests 10k tables, this is the course they're taking. And it's wrong.



So here's my bit of teaching for the day:

SQL is about sets. You should really consider that the power of SQL is in its ability to handle sets quickly and easily, and in the ability of the language to parse for the relevant matches to a set of query parameters. What this means for you is that the intent of SQL is to have one massive table of all blog posts (to pull a single example, that may or may not be appropriate) and to select the matching blog posts from the table by query.

Additionally, you ask about open files, but that's just it, by doing what I suggest above, you have at most four tables to worry about open files on. And it's "how the big boys generally solve this problem" if you're really curious.

But the fact that you're asking about open files and other micro-optimizations leads me to think that 

The real point I'm trying to make here is this: Don't try to re-engineer the database according to what you think would make it optimized, because you're not a database engineer.

While this may seem to be a bit harsh, it's not. I assure you. If you were a database engineer, or worked on a database core-development team, you would already know the answers to the questions. Thus QED. But you have to understand that this is what it sounds to an experience DBA like what you're doing; this trying to optimize the database by theory rather than rational approach.

Now, having said all that, and having been a bit harsh, and having seemed to reject your request outright, I'ld like to ask for more details so I can really focus on answering the question you've asked, altho, if I can hazard a guess, you've gone and ignored everything I've had to say after the second paragraph.

So with that in mind, here's what would make this question a little more answerable:

What platform are you running this on? How many disks are there? What size and speed are they? What version of the OS? If Linux, what distro do you intend on running? Will this be in a VM? Will it be supported for updates in the future or do you need a prop-once and forget box? (meaning negligible long term support budgeting)

And if I may ask, what framework are you using for this database that it will have 10k tables? I ask for personal curiousity.