Pathfinder --
You'll also find that you can afford to play a lot more relaxed in a larger galaxy; there's a much greater survivable margin of error there, and you need not play completely ruthlessly to win. You can even use Ministers (well, transports, mines/sats, resupply and repair, anyway) and win.
Also, tailor your race to your intended strategy. If you don't think you'll be doing ground combat (either attack or defense -- but I've not yet seen the AI try, so mostly attack), you can safely take a -50% there. Research bonuses are GOOD, unless you're going to try to blitz (small galaxy) and need production / combat / maintenance bonuses instead. If you don't intend on using trade that much, you can take a -50% on Politics. And so forth.
And you might want to think about phases of the game -- early expansion, boosting research and production output, converting atmospheres and so forth. And what's the baseline warship that'll suffice should somebody come a-knockin' -- phased polaron beams are pretty good for this, since they're not that costly to research, they're common enough that you might be able to steal them, and they do quite well (when combined with PD) throughout most of the game. You don't want to get stuck with DUC Is, but neither should you feel compelled to go for Crystalline X or whatever just in case.
In my current, _very_ relaxed game in a 255-system galaxy, I started in a rapid-colonization phase with an emphasis on getting better applied research and economic techs.
After this, came getting the other colonization techs. My race is Organic, so it behooved me to get as many colonies as possible in preparation for the replicant centers...
Somewhere along the line I became Mega-Evil w/o ever fighting or doing anything remotely evil, so I needed to switch focus to getting some combat techs due to having two low/medium-intensity wars on opposite sides of my empire.
Once both were safely contained, computer techs followed to maximize production efficiency, because what I had in mind would be expensive -- atmosphere conVersion (there *really* don't seem to be that many Large/Huge with no atmosphere). War came again (when I found the Eee, who had roughly caught up in score while I was at war). However, their ships have vastly inferior range (since mine have solar collectors, and can destroy the nearby colonies they might use for resupply; basically, the Eee entirely on the defensive), the advantage was clearly mine. Mega-Evil got triggered again, while the first phase of atmospheric conVersion is under way (gradually queued 'em up in the first 10 systems. One atmosphere already destroyed, the rest will follow. This should help my pop and resources skyrocket...).
The plan for the rest of the game is to
a) convert more atmospheres (eventually, all the domed colonies -- namely, almost all my colonies)... This can be done relatively safely since there appear to be no serious threats (although much of the galaxy is still unknown, so there would be room for an annoying Darlok clone).
b) convert extra space into more resources, research and intel (miscalculated; need more radioactives, in particular. On the bright side, minerals are abundant.)
c) refit my aging warships with the combat tech I'm researching now (since pretty much all the efficiency tech -- Computers, Planet Utilization, etc -- are already maxed. So are some of the useful, but not yet used, shp techs.)
d) unleash them once more on the Eee and anybody else who stands in my way.
Could probably jump to this now -- at least, the Eee -- but that wouldn't be as satisfying.
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-- The thing that goes bump in the night