There is no exception for traditional 401(k) withdrawal limitations for first time home purchases; if you read that somewhere, you read incorrectly. If you take a distribution from your traditional 401(k) to purchase a home, you will pay taxes and a 10% penalty, even assuming you're able to at all. The first-time homebuyer exception is for IRAs, not 401(k)s. See this article for example.
The IRA exception is mentioned in Tax Topic 557, and the 401(k) etc. is covered in Tax Topic 558. Note that the first time home buyer exception is mentioned in 557, and not 558.
You may be able to take a loan from your 401(k), but it would have to be paid back (to the 401(k)); that isn't something that only happens on home purchase, but it's risky - in particular in that you have to pay back the full balance immediately if you leave your job, or face the penalties as above.
All in all the 401(k) loan isn't a great option for homebuyers as it involves risk (both that you have trouble paying it back and that you leave your job).
That said, if you're not getting the full employer match, this option is a reasonable one as you do end up ahead (even if you take a hardship distribution, you're still ahead since 10% is less than 50%). If you do this, check your 401(k) plan documents to verify that either the loan or the distribution is possible, and what the terms would be.
Alternately, if you have the ability to contribute to a Roth 401(k), you may be better off, as you may be able to withdraw contributions tax- and penalty- free, assuming your plan allows it (the IRS does, in any event). Check with your plan for more details and to see if it's available. The employer match would always be non-Roth, so not penalty-free, but your own contributions would be penalty-free.