My start is better. I use the cash to rush out colonies and constructors in order to secure my early territory faster. Scout with survey and a scout or 2.
Good. Most people I think hold back some money to
- hire a survey mercenary (when they find bazaar)
- endure the early-game deficit spending.
As for Tech I usually grab some research tech, colonie tech and diplomacy. I slowly get into military.
Good, but do not grab research techs in the beginning. They take a long time to research and do not give you much early-on. Instead, I'd suggest getting techs that increase your ship speed (under Engineering).
Problem: I get into serious money problems despite building markets. Getting more anomalies helps but I feel like I am missing something. Maybe I need to run both market and tourism?
Happens to all of us. Anomalies and some money in the bank are really the only ways to get through this early deficit phase. If your government allows to send missions, you can also build treasure hunts at your shipyard.
Do not build markets in the beginning. Build morale buildings (entertainment centers, ideology buildings) instead, so you can increase tax rate later. Due to how game mechanics are now, this is much more effective.
Tourism is great, but you have to research it first. At the very start, you can only build Import-Export center on one planet. Remember that Tourism scales massively with the number of your colonies that have Ports of Call built. So, as a rule of thumb: if you only have very few colonies, Tourism is not very important. If you have many colonies, research it ASAP and build Ports of Call on your planets. It will then quickly solve any money problems you have.
But keep in mind that Tourism is tied to tax rate like everything else. So you should have enough morale on your worlds to increase tax rate.
Next big issue is military power. If I do try to get tourism as well my military is already behind so it will be more behind. How do I manage military? just constantly make small hull ships for a while? The transition to medium and large hulls is also a question mark for me. My management in that area is clueless.
Yes, build tiny or small hulls equipped with the basic missile early-on to get your military rating up (so that the AI doesn't target you). Transition to medium when you have to do some actual fighting (then you should also get some Logistics tech and train a Commander).
Large (and huge) hulls are not really needed, they are just "icing on the cake". You can win any game using medium hulls only, so you can research large/huge whenever you want. If you want to use self-healing ships, large hulls are pretty much mandatory though.
Military wise I am behind and will likely get smashed soon now that the Yor are dead and done distracting the other Leaders.
Try to avoid getting into that situation. Once you have researched a few military techs, you can build tiny hulls with an attack value of 8 or so. If you alternate between building these and the other ships you need, you can keep up with the AI in military rating (though probably not on the two highest difficulties).