FirstNissan,
The best way to select any system is to resolve a few questions. You've already answered a couple:
What are your music tastes? You listen to classical. That means a balanced system, and where you need to give up frequency range for cost, you should sacrifice equally at both extremes. You should also pay special attention to dynamic headroom, as classical has a wider loudness spectrum, and broader dynamics than other types. But with radio, you will already lose both frequency range and dynamics, so you may not need to work as hard on this factor.
What is your room size and preferred loudness levels? This will dictate the critical speaker/amp relation, and may limit the former according to relative SPL efficiency to get the levels you like.
What is your budget? You've already given that.
Note that every piece of equipment has its own "voice" or tonal and timbral signature. The trick is to know what they are in advance so that you can balance them to taste. The touchstone to good matching is "synergy", with strengths and weaknesses balanced off. It is why you don't mate a classic K-horn to a Krell (shrill), or an old Vandersteen to a CJ (too relaxed and warm), for instance . . . unless you like those results.
The front end also plays a part in the equation. Certain front end sources dictate different choices the rest of the way. You haven't identified what all your sources are. But since you are listening to radio, that factor will be built into the amp choice by necessity with any receiver.
But at your budget (and your listening tastes), I would err towards warmer (sometimes called "musical") electronics, as speakers (particularly more modern ones) tend to be a bit unrefined and unbalanced at those prices. Because you want radio, that means a receiver (and not separates) at that price range.
Perhaps an early Marantz (post-Saul) receiver (1970-74), or maybe a later "b" variant, or a similar-timbred capacitor-coupled output amp. These models are a little more forgiving of a bad tonal speaker pairing. While there are even better sounding receivers pre-1970 (Fisher stuff in particular when Avery still owned things), they will require repair/reconditioning that you probably can't afford. H/K still made some decent gear into at least the mid-70s. Same for Fisher. Avoid both by the late '70s. That was the "power wars" era. Once you start getting into the era of "quartz" and other digital tuning, the tuner and the amp section quality starts to fall off, unless you buy higher up the food chain. There are some decent NAD "chicklet" button receivers from the mid-later '80s, for instance (but not as nice to my ears as the older ones). Rotel can be hit or miss, but they have a few good ones from that general period. Same for some Onkyos from that era, or earlier. I don't care for Pioneers, Sonys, Kenwoods and some Yamahas from that period - big names, small sound. My receiver tastes fall off the table by the mid 90s, so I can't help you much with later receivers. They all pretty much sounded bad to me by then, and one is better off with separates. Receivers haven't gotten any better since to my ears. Lots of buttons, lots of inputs, dazzling "Toyko at night" styling, lovely measured specs . . . but thin, mediocre quality sound. Loud can only cover up so much.
There was a sea change in two channel electronics audio quality at the mass and mainstream market levels in the mid 1990s as the first wave of multi-channel HT gear started rolling in. Some of it was not very good unless you were very careful. Traditional "Hi-Fi" and two channel audio was forever degraded at the mainstream as a result. Those familiar with the golden era of stereo and earlier will understand. So perhaps that is your cutoff.
Alternatively, approaching it first from the speaker side, if you are aware of the foam surround issue with them, the small to midsize Advent bookshelves from the early to mid-1980s are a cheap but forgiving "all-rounder" speaker that sounds decent with most equipment, including many newer dreck amps.
If it must be newer, one economy priced "sleeper" small bookshelf speaker of later vintage to consider is a used original Ascend CBM-170. Ugly as heck, but a balanced range, good sounding little box. Relaxed yet still articulate. This sold new in the $300-400 range, and was better than comparable B&W, Mission, and KEF models. Generally though, look to the UK and Europe for the better sounding later small bookshelf models.
And don't laugh at this last one, but there are actually some older console units from the '60s into the early '70s that don't sound half bad. Big, honking pieces of furniture from Magnavox and Fisher, or even some German Grundig units, that grandparents and estates are now sadly kicking to the curb. Some enthusiasts drool over these just to get the electronics out of them, some of which are tubed, some of which are outstanding. Some are fine pieces of furniture in their own right. Speaker quality varies, but a $2000+ Fisher "President" console from the early '60s (cost about what a new car cost then) still makes good notes. I have mixed emotions about gutting a good working console, but at least some of it lives on. No, it's not high end sound as "audiophiles" would have it, but if you've got the room, it's one way to get a good-sounding complete system (that sounds better than any other later all-in-one rack or stack). . . sometimes for free. It will certainly turn guest's heads, especially now that "mid-Century" interior design has regained some urban appeal.
Those are just a couple suggestions. There is so much good used equipment still out there that you could come up with a thousand good sounding alternatives.
