As a general rule, I'd also go with separate instruments. While you can get a scope with a competent meter, by the time you really do, you're probably paying more than for an entry level scope and a meter. I think the one good argument for combined instruments is a portable workbench where getting a lot of equipment in a small/simple to setup package is important... but I think fairly few hobbyist applications really require this.
For the kind of budget you're talking about, you may actually be able to find an entry level scope and a 5 digit used bench meter, unless you're looking for a really high spec meter, you can probably get a very capable one for a lot less than you're currently budgeting.... something like a Brymen BM235 and a Rigol DS1054z is probably about your total budget new and offers a lot of capability.