My solo-games are usually played at Emperor/DG level, with Mostly-/All-Random starts (apart from size and maybe landmass-type), and then "play it as it lays", rather than re-rolling until I get a favourable start (with Rivers and Cows galore!). That does tend to mean that the VCs I pursue/achieve will tend to be those that don't need to be planned for from the start: militaristic (Domination, especially on Pan-maps, but also Continents and occasionally Archipelagos), or scientific (Space if Cont, UN if Archi), rather than cultural.
On the grounds that while the AI-Civs can be a nuisance while they still own adjoining land, but tend to suck (worse than I do!) at overseas invasions, for every game I will aim to achieve exclusive ownership of whichever land-mass I start on, ideally (long) before the end of the Industrial Age. How many turns (and how many wars) that will actually require obviously depends on multiple factors: map-size and -type, size and geography of my landmass, number/ proximity/ identity of adjacent Civs, availability of freshwater/ resources near my start, my Civ's traits and UU, etc. But in general (and since Emp/DG-AIs start with multiple free def/off units), by the time I have 2-3 additional towns placed and growing, I will already be gearing up for my first war, with the best attack-units that I can build (even if only Archers) — because I will be expecting that war to happen very soon, one way or another.
My explorers should also have gained sufficient knowledge of my immediate surroundings long before then, that I already know which direction(s) I'll need to prioritise my development/ send my forces, but I will almost certainly still be suffering from the Despot-penalty, which significantly limits the distances at which additional expansion/warfare is still going to be 'profitable' — especially while my Civ is still small, and/or I still only have foot-units. I probably won't yet be able to maintain a firm hold on territory which is a long way from my capital (say, 4th-ring distance at CxxC placement, or 4 turns' worth of foot-unit moves) — and if I'm still Despotic, any such captured towns likely won't be returning much in terms of income/shields, either. Most of my early wars will therefore be opportunistic, e.g. forced by 'Leave or declare!' demands, or (a bit later on) triggered by alliances (mine or theirs), and necessarily limited, rather than campaigns of extermination.
The first offensive war that I initiate, will therefore usually not happen until my borders meet a weaker/equal AI-Civ's borders — and its purpose will either be to obtain additional expansion-room for my own Civ, and/or specifically a Strat/Lux resource that I need/want, and estimate that I can take and hold with what I have. Such a war might be fought to capture a resource-town(s) founded in my backyard, and a long way from the parent-Civ's capital (so that by the time the AI-Civ's troops arrive, their Dear Leader is already prepared to sign peace with me).
Conversely, if I'm attacked before I was 'ready' to start a war myself (e.g. because I rebuffed a tribute-demand), I would usually just aim to fight a successful defensive action initially, to whittle down the attacking AI's excess troop-numbers to parity with my own, and then sign peace at the earliest opportunity (while also moving that AI-Leader to the top of my *hit-list!). Of course, if the pRNGods smile upon me, and I manage to kill enough enemy attack-units to tip the balance of power into my favour, then my healthy attackers might start/ continue to press forwards, in order to do as much damage as possible to the offending AI before I become unsustainably stretched — this way, the AI-Civ will be more likely to offer additional/ significant concessions for peace (such as their gold, Workers, techs, or towns).
Once I've begun to build decent fast-units (e.g. GalSwords, Horses/UU-equivalents, ACavs, Knights/UU-equivalents, or Cavs/UU-equivalents), that's when my expansion will begin in earnest, and at that point, wars will only be halted 'prematurely' (i.e. prior to the enemy AI-Civ's complete defeat!), if e.g. war-weariness or SOURs force me to do so.