I like the Scott integrateds. I had a 299A and have a 222C. Both areI very good. Classic sound. Really musical. Both these amps used EL84s or one of the variants.
Also, the Eico HF81 is supposed to sound great. This is also a EL84 amp. I have a fixer upper unit that I have yet to get to. Haven't actually listened to it since it itsn't working, but many have advocated for this amp.
Actually, if you're interested in the Scott 222C, I would sell it to you. Please PM me for details if you're interested. I bought this for my brother and ended up setting him up with something else. It's now safely locked away unused.
As for speakers, I'm very happy with the the Klipsch Heresies that I have. I would recommend them to you, but these days you'd be lucky to find a pair cheap enough to fit into your budget.
I bought my vintage pair in the mid 90's before too many people rediscovered vintage Klipsch horn speakers. Paid about $250 for the pair. If you can find a pair for that much, grab them. One thing to note, though, is that the sound they make has a certain personality which you may really like or may really dislike.
Good luck,
KT