I think you're going to have a problem finding an acceptable espresso machine and grinder for $300 (at least a traditional semi-auto + grinder, there are definitely other options if you want to buy some gear without motors in it). Although if you were to look in the $5-600 range you could probably find a couple options that would work, then you could hunt on ebay or craigslist to find some deals on used equipment, which might take a while.
By searching online, and waiting for deals I was able to get what I would consider about the bare minimum espresso gear for $400, not including a tamper, steam pitcher, etc. When I upgrade I'm looking in the $2,000 to $4,000 range for a new machine and grinder, which should give you an idea of the range of prices that you can pay for home espresso gear (with an entire layer of more expensive pro gear above that).
When you're thinking about your budget be sure to keep the price of beans in mind. I'm sure that over that last two years or so I've spent more on beans then all my equipment put together, and buying good fresh roasted beans is definitely worth it. If I go from a $200 machine to a $2,000 machine my espresso isn't going to be 10 times better (maybe 1.5 to 2 times as good, and more consistent). But if I go from $6/lb beans from the supermarket to $12/lb artisan roasted beans the espresso will be at least twice as good if not more; it would probably go from "unacceptable swill" to "good" or at least "above average" with the occasional great shot if I'm lucky.
And if you want an excuse to spend more, take a look at how much you're spending on espresso now, if you're buying a couple lattes a week, that can easily add up to over $500/year, all that money could go to making espresso at home instead
