Hey you want to bump this post to get some attension...

What should I be putting on my homeworld? Is it best to have a good mix of buildings?

you should put a good amount of factories and market centers on your homeworld to get a decently good start without your economy crashing almost intantly.

What should I put on the smaller class worlds with only 3 panels?

On say mars which has only 3 avaible tiles you should put every square a factory and start building ships as there is no other useful benifit to somthing with so little space available.

How do I get the other races to be my allies or keep them friendly besides throwing money at them?

Wow! someone actually asked how to keep relations high? you really need to just be a good trade partner send some of your frieghters to there worlds and trade with them frequently... giving gifts will almost certaily improve relations at anytime...

To keep people happy on a small world (like Mars) do I need Entertainment or can I keep them happy without it?

really there is cap to population on some of these planets but you can transport more people there if you like to keep anyone happy lower you tax rates and that should help the most on those small worlds (actually more like hardly habitable worlds) ..

In addition to El Conquest's tips on relations:

Researching up the diplomacy tree helps out your relations with other races. The more you can talk to them in a way they can understand, the more friendly they will be. Also, having a moderately strong military is also important. Races tend to think poorly of you when your military is weak, and they will often attack you for just that reason alone. Make sure that you are in the middle of the pack, or slightly ahead of most races militarily, and you will have favorable diplomatic relations with them. (If you get too far ahead, you may be considered a threat and ganged-up on.)

To ally with other races, your relationship has to be "close," which is one step above "friendly."

Final tip: having a good or neutral alignment makes an alliance victory easier, as other races tend to like you more. It is harder (but not impossible) to win an alliance victory with an evil race.

i ususally try for conquest victory on larger maps high difficulty.

I like two factories and a starport on every world.

On a world larger than 4 , I also place one research lab and bank and the rest factories. That way, as you techs increase they get auto upgraded.

I place factories or research on those bonus tiles and I build specials and trade goods wherever I can build them the quickest.

I select a big planet or high manuf bonus planet as my manuf capital and a large world, usually with research bonus as my tech capital.

I try not to build any morale or embassy or farm improvements until I need them.

I always try to get eyes of the universe and aphro and grav accelerators as they are decisiv advantages. Eyes of the universe is really important becasue you cannot trade for it and it elimantes the tedious need to tend to scanners irrelevent.

For Eyes of the Universe you need to research Sensors IV, for aphrodesiac you need to research Habitat Improvement, and for gravity accelerators you need to research Zero G Sports Arenas.

I always put at least one of each thing, on every planet, if they fit.

Ah, the good ole days of Gal Civ I....

I usually build only factories and research labs on all of my planets. I then research trade and a bunch of range techs, build up a fleet of tradeships, and then send them all off to the farthest planets in their range.

...Of course, I usually end up in debt, so whatever works for you is probably better.

Wow!

Thanks everyone, one of the great 'features' of this game for me has been the helpful community

Most of the time the home world should be designated a economy world. Follow the basic outline for all such worlds.
2-3 factories - most other tiles markets. Homeworld has an implicit farm in it so one extra entertainment building is needed. When you reach pop max convert one market into a farm and another into an enterainment building.

Of course, special tiles mean you might have in effect more tiles to play with.
E.g. A manufacturing 300% tile means that you could survive with just the one factory. A farm 300% tile is possibily a waste though on your home world as you'd end up needing 4 morale buildings just to keep up.

Small worlds can be useful as small ship (or pref transport) producers, research worlds or economy worlds. My personal favorite is ressearch... but they can add a little to your cause as any of the above. Just don't spend too much time worryong about them. They are exponentially less important that bigger planets.

Early on relations are based almost entirely on military strength. Once the first year is over you'll have had chance to build up your diplomacy from the diplomatic techs. Build spin control ASAP if you are going the diplomatic route. It buys you a lot of time... and it is on a tech path you will be concentating on anyway.

On mars you can build a single factory and then build a farm or two and then once you got those farms build another farm after you demolish that factory or perhaps a happiness center, you can use it for a tax base and make some money cause you cant make much else there, if you use a colony ship buildt on earth, obviously you'll be building em there at some point, you can ferry excess ppl from earth to mars cheap and easy, just move em 499 million at a time, once you get to mars the other 1 million are like monopoly jail "just visiting" cause it takes 1 million colonists to move a colony ship did you know that I bet you didn't hows this for a run-on sentence, I'm not even going to use the comma anymore so there!