Keep your speakers for now, they were very good in their day, and a god design never dates. Not much anyway. This gives you a chance to buy better electronics - rubbish in, rubbish out.
You have plenty to choose from. Cyrus, Naim, Roksan, Rega, Quad, Arcam etc - they all have CD and amp combos in your price range.
If you want to keep it simple and small, try the Quad CDP2 and 99 power amp. Two midi sized slimline boxes with a nice smooth sound that's listenable for hours on end. Rega is similarly smooth, and one of the best pairings musically for the money. Roksan's also laid back. Naim is a littel more exciting than those previously mentioned, with a little more sparkle, and probably our most popular combination at this price point. If you can pick up a recntly discontinued Cyrus amp and CD player, you'll get good value for money, and these have a leaner, more forward presentation suited to those who like their music to demand their attention.
Judging by your current system and what you're used to, I'd try the Quad, Rega and Roksan one initially, then try the others if these aren't doing much for you. Take your speakers along for a demo as you'll be able to try tha out against something more modern to see if you think they're worth changing. They probably will be, but holding on to them a bit longer means you'll have a better system long term.