Sydney to Canberra is good-quality freeway all the way.

Sydney to Melbourne is mostly dual carriageway, freeway or near-freeway standard, although there are a few short single-carriageway, one-lane-each-way sections between Goulburn or Yass and Albury in New South Wales (at least there were a few years ago). Even these sections are generally adequate.

Sydney to Brisbane is more mixed. It is a good road (freeway or good-quality dual carriageway) to somewhere north of Taree and then again four-lane or dual-carriageway in southern Queensland. There are some substandard sections on the north coast of New South Wales (substandard for the amount of traffic that is carried). That is the coastal route. In fact, I prefer to drive from Sydney to Brisbane via the New England Highway through Tamworth and Armidale: more single-carriageway sections but the road is much more equal to the (lower) volumes of traffic.

Speed limits are fairly rigorously enforced, mainly I think by marked police cars, radar and cameras. In particular the police are very strong on people who do not obey the posted speed limits on the outskirts of built-up areas, even though the reduced limit sometimes comes in ridiculously early. (No towns on the road between Sydney and Canberra or Melbourne, some between Sydney and Brisbane.)

Speed limits on freeways are generally 110km/hr; on non-freeway country road they are variable and in some cases they vary frequently. In towns the normal limit is 50km/hr, although on main roads it is usually 60km/hr. (If not signposted as 60km/hr it is 50km/hr, though.) If you drive through a town be wary of the 40km/hr limit when passing schools at school-in and school-out times; these zones are signposted with the limit and the times.

There are lots of lorries on Australian roads. In general these are not likely to be troublesome on the routes you mention except in some parts of the Sydney–Brisbane drive. In the single-carriageway sections there are sections with overtaking lanes every few kilometres, but you can get stuck behind a slow vehicle in between these overtaking sections.

Rest stops and service areas are plentiful enough and usually reasonably pleasant.