Am I simply out of luck in finding a cheaper solution here

to be blunt, yes. You'll need both phono pre-amplification- to bring your u-turn up to line level- and power amplification- something to turn line-level into the acoustic impulses that drive your speakers.

Sometimes they are integrated into one unit, such a with a receiver, which contains an AM/FM tuner, phono preamplifier, and something called an integrated amplifier- which consistes of sound control (volume, balance, bass and treble controls, and switching between various inputs) and the power amplifier needed to drive your speakers.

You could buy the phono preamplifier separately, however you will still need the integrated amplifier to drive your speakers and manage basic functions like volume level and tone control. IMHO if your primary way of listening is on speakers, an integrated amplifier with built-in phono preamp is the best way to go.

The recommendation of a receiver is a good one, since you only need one box to achieve all the functions you need, though there is the extra tuner part. However, a reciever and pair of speakers is how the vast majority of the listening public listened to their vinyl before the advent of relatively inexpensive, small-sized personal computers. So there are millions of used receivers still in service today, and many decent units can be had for not a lot of cash. For instance, there is a perfectly functional (at least represented as such) 20wpc Technics SA-101 receiver for sale on Ebay for $30 right now. It would be perfectly adequate for the your purpose.

Just bear in mind if you buy used, you need to expect occasional servicing- this unit was made in the early 80s and components will fail.

It might be more cost-effective to spend the $200 now on a decent basic integrated amp and enjoy the full longevity of the new components and maybe even a warranty if you're lucky.