Interesting question.

Our best source of knowledge for Sullan veteran settlement in general is Pompeii, in Campania. There, we find that the general pattern seems to have been that veterans settled on farms outside the walls of the town, while the "locals" (in this case, the Oscans) seemed to have moved into the city proper, within the walls, perhaps to find new trades. This is the general trend as far as we can tell. We see a general trend of deliberate "Oscan" elements in the architecture of private homes within the walls after this time, particularly among domestic spaces (like the earlier traces of the House of the Faun), probably an attempt to reaffirm local identity. By contrast, the public edifices become decidedly more "Roman" in the second half of the 1st century. Out in the farmland, we find archaeological evidence that some of the Sullan veterans constructed new farms in new areas, for whatever reason; in other cases, older Pompeiian "Oscan" holdings were occupied and remodeled. The land was almost certainly put under new cadastration--that is, the borders between plots was forcibly redrawn and redistributed when the veteran settlement in the area was organized. Cadastration was a normal part of Roman occupation of a space and one of the more recognizable consequences of the Roman colonial process. The actual land itself was a hodgepodge of formerly locally owned plots, ager publicus ("public" land nominally owned by the State), and the possessions of those who had fallen victim to Sulla's blood proscriptions.

We assume that the situation was the same in the north. Faesulae famously received treatment similar to Pompeii, and it seems that again the locals were pushed off the farmland and into the town. A fragment of Granius Licinianus, though written two centuries later, hints at the details: Faesulani irruperunt in castella Veteranorum Sullanorum et compluribus occisis agros suos receperunt. et in senatu defendebant, quod vulgus agreste domoque extorre eo coactum esset. et consules dato exercitu in Etruriam profecti sunt[.]

"The people of Faesulae burst into the fortified areas of the Sullan Veterans and, with many killed, recovered their lands. and they defended [their actions] in the Senate, on the grounds that the rural peasantry had been forced to this end after being driven from their homes" (Licinianus 36.36)

The mention of the castellae is interesting--fortified strongpoints out in the countryside for mutual protection, like would be found later throughout Medieval Italy? Perhaps they were just farmhouses, which would take on the appearance of a fortress. At any rate, we get the sense that the situation was similar both in Pompeii and in Faesulae.

As to OP's question: in both cases, we see that the veteran settlers had initial capital. They were either remodeling older farm holdings, or they were constructing entirely new ones. These might have been the castellae, or perhaps the castellae were also constructed. We don't have a document which specifies how and where the soldiers were enriched, unfortunately. Those who had gone with their general to the East would have benefitted greatly--Sulla's antics in Greece when facing off against Mithridates were generally characterized by plundering. Some might have become enriched as participants in the proscriptions themselves, though I struggle to imagine that they could have numbered enough to represent the whole category.

As far as transport to the plots: I think that goes into the same category as the general capital required. The soldiers would have acquired help, either hired or slave, and the means to transport themselves, their families, and the materiel of their new lives with them. It was probably very similar to the wagon trains that infiltrated the old American West, and probably in similar group formations.

The case of Faesulae can serve as a posterchild for the sentiment across Italia in general: open hostility. The veteran settlers in Etruria had a terrible time, were rightfully resented and mistrusted, and were generally prevented from leading the happy rustic life Sulla had awarded them. Even without the open violence of Faesulae, there must be a certain degree of harmony between urban and rural in the Roman economy. The Sullan settlers would have been excluded and railroaded at every turn, as indeed we hear about in Etruria. We hear that many Sullan veterans had already lost/sold their plots by the next generation, and many that still hung around became soldiers in the subsequent political upheavals. For Faesulae and Arretium, it was specifically in the ragtag rebel army of Catilina under the old Sullan veteran Manlius. Some argue that it was not the Sullan veterans themselves, or their strained relationships with their new neighbors, which are to blame, but general economic hardship in Italy.

For more, see:

Thein, "Sulla's Veteran Settlement Policy" in Militärsiedlungen und Territorialherrschaft in der Antike (Topoi / Berlin Studies of the Ancient World 3), 79-99. Berlin: Walter de Gruyter, 2010.

Santangelo, Sulla, the Elites and the Empire: A Study of Roman Policies in Italy and the Greek East Ch 4: "Pompeii and Campania Felix." Leiden: Brill, 2007.

...and Santangelo's PhD thesis which formed the backbone of the above, "The Impact of Sulla on Italy and the Mediterranean World," University College London 2006, which you can read online here. There is a very nice writeup of what we know (and don't know) about Sulla's settlement of veterans, with a nice attention to the contrast between the situation in Campania and Etruria. And everything is very well cited and sourced, as expected in a thesis.