Hi and welcome to AK!
A couple questions. Are you handy? Have basic tools? Can you solder?
I don't want to overwhelm you, but some info you should know before buying vintage speakers.
If you decide to go vintage, there's a good chance you will need to do some work on them. Usually the old caps need replacing as they are out of spec, woofer surrounds have rotted and are gone. The woofers will need new surrounds installed. Most speakers in the smallish book shelf size have relatively simple crossovers, making cap replacement fairly easy. There are tons of videos showing how to replace woofer surrounds. Not to difficult to do, but you must be very careful to center the voice coil when gluing the surrounds to the woofer frames, known as baskets.
Some vintage speakers like KLH and AR have cloth surrounds. They don't need replacing, but often need resealing with a brush on sealer. They have simple crossovers, and are excellent sounding when restored.
ADS is another great brand, with great sounding speakers. There are a ton of models that would suit your needs quite well. Generally, they hold up well, not requiring much work to enjoy them. Most use rubber surrounds so you don't need to worry about replacement. Their crossovers are a bit more complex, but they used good film caps and usually a lytic cap that is usually ok, but would be a good idea to replace at some point.
I have all three brands I mentioned, and all are excellent. Many can be found well within your budget.
Newer speakers also sound great, are usually much smaller than vintage "book shelves". The obvious benefits are they won't need restoration work, but many may need a small sub for the deep bass we all love. This will add to your budget, but doable.
If you decide to go new, read reviews for speakers in your price range, then ask for opinions here from actual owners. You'll get much better feedback than from manufacturers marketing hype.
This is an addictive hobby, extremely enjoyable searching for and restoring various projects as you get into it more.
Glenn