Visigoths - originally, as Feoderati under the Romans, they established area of rule in Gaul and Spain. The early (but exciting) campaigns of Alaric I predate the period considered here. In 507, however, the Franks, under Clovis I beat the Goths (under Alaric II) at the Battle of Vouille Visigoth rule in Gaul was at an end, but the Frank's were established as a kingdom that would give us Charlemagne, France, Germany, and a lot of different kinds of cheese.
The Visigoths, however, survived the loss of Gaul. They had a kingdom in the Iberian Peninsula (Spain, or Hispania). There, they survived (and in harmony with the rest of Christendom after converting from Arianism in 589) until being overrun by the Moors (Berbers and Arabs up from North Africa) in about the year 711 or 712 (the Mozarbic Chronicle of 741, written in Latin, is unclear). That was the Battle of Guadalete between King Roderic of the Goths, and Tariq ibn Ziyad.
So, for about two hundred years, there was a gothic kingdom in Spain. It gave us a lot of interesting Gothic architecture and early cathedrals, but not a lot of details on military practices.
Looking at what wargames have to offer on the Western Goths is interesting. Again, turning to the original DBA list (as a conceptual distillation of the 1982 WRG army lists, and benefitting from eight years of further research and debate) we see that there is an infantry core of five elements. These can be either spear, or warband, or a mix of warband and auxilia - depending on which allies or sources you prefer. But that establishes a solid infantry battle line, supported by two units of skirmishers (Psiloi), and finally a solid mounted contingent of four units of four Cavalry units, and a Knight (general) unit.
This could easily represent the army of Roderic, at the battle of Guadalete. There, his solid infantry line was a match for the Moors, but he lost because his right cavalry wing under a disgruntled commander abandoned the field allowing the numerous, but lighter, Moorish cavalry to flank the infantry line. Legend replaces the commander with Count Julian, who turned traitor because his daughter was raped at Roderic's court, but this (while a great medieval narrative) is unsubstantiated.
Refighting Guadalete as a decisive battle that ended Christian rule in western Spain, until the Reconquista, is a worthy war gaming goal, but the lack of other major foes makes the prospect of building a large Visigothic army seem like a futile enterprise. It is, however, a great example of a balanced army from the Barbarian Kingdoms era. There are, of course, lots of Possible match ups against sixth century foes, such as Byzantines, Ostrogoths, or even early Andalusians from the other parts of Spain.
For figures, standard dark age infantry (metal conic helms, round shields, and either sword, spear, or bow) make the battle line and Psiloi easy to model. Likewise, the cavalry (cloaks, metal helms, round shields) are readily available. The older Minifigs heavy barbarian horse and heavy barbarian infantry are nearly perfect, as well as many modern manufacturers.
A nice set of pictures of a painted army is here.is here.