If you want a classic-feel you can look for (pretty old now..) amiga 1200 or 4000 and equip it with (bit more modern) powerpc card (up to 233mhz) and pci bridge (prometheus, mediator, grex) to use some pci cards from pc.
moving on in time: there is amigaone, someday with os4 and pegasos with morphos (already released). while decision which one is better - aos4 vs morphos is controversal, in hardware terms pegasos clearly seems to be a winner. release of next pegasos is planned for september and if plans come true it will signifficantly better hardware for half that price (starting from 299euro!).
If you dont want to invest in hardware you may try amithlon (watch it! its commercial). Very fast, but not-so-compatible amiga emulator for pc (does NOT run under windows, boots pc off cd) or AROS - amiga-like, but NOT amiga compatible (AROS for pegasos will make more sense
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So there is a lot of amigas and amiga-alike systems. (...but no good web browser :/)
