Community member Waervyn has made some pretty good short tutorials that could help:

I highly encurage going for an economic victory if you are playing on higher difficulties, but when you go to war their ships are quite costumizeable. (at the cost of 25% extra production time)
I played as the Horatio two days ago on max difficulty (without pirates :P) against the Vodiani and was lucky enough to get really friendly with them so I didn't have to develop any millitary tech at all. 

About colonisation, yes build as many colony ships as you can early on bacause you can colonize just about any system you see from the get go. (assuming you play on a galaxy with plenty of telluric planets). I highly recomend getting the bonus +happiness-dust law from the verry first turn as empire-wide happiness gives a bonus to food and influence production, making the food strain on your original system less of a problem. Horatio also get bonus happiness from hot planets (witch gives alot of industry as well) so colonize systems with alot of those as indusry is the basis for all future development, alternativly you could colonize planets with alot of food, further lessening the strain on your surogate system.
For system development you should go for food and industry from the get go ensuring you can expand rapidly (I also recomend playing on a big map because its less cramped -> hostile).

Hope this was helpfull! :)

Early game with horatios is one of the harder for me. So i focus on colonization and creating a heavy science/production/food base for my empire. I try to avoid to loose time by making army, and avoid as much as i can war. I even give to threatening IAs what they want. I deal with pirates with low cost and specialized armies. Sure i am a coward, but i am still beautiful. If i am confronted to cravers... Well. I didnt win in this situation already. I think the strategy during war againt craver is to just defend, avoid fight as much as possible, commit into war as little as possible, and try to increase your empire global power the most you can. 

After the first phase i focus mainly on influence, convert the most minor faction i am able to. Make peace with all IAs if i can, get maps, convert more little factions via maps. Then i am kinda free to do what i want. 

Expand early. Explore actively, you can even replace explorer's weapon with another probe module. Befriend minor factions for Dust and genes. When your planets are well-developed, conquer major factions' genes and hear the lamentation of their rhybosomes.

i spliced craver genes for a +4% FIDS per pop....holy crap!