I am assuming Nicea was an ecumenical council. Who decided who should go and who couldn't go to Nicea? How was the council of Nicea paid for? Who opened the council and presided over it?
Character and purpose
To most bishops, the teachings of Arius were heretical and a danger to the salvation of souls. In the summer of 325, the bishops of all provinces were summoned to Nicaea (now known as ?znik, in modern-day Turkey), a place easily accessible to the majority of them, particularly those of Asia Minor, Syria, Palestine, Egypt, Greece, and Thrace.
Approximately 300 bishops attended, from every region of the Empire except Britain. This was the first general council in the history of the Church since the Apostolic Council of Jerusalem, which had established the conditions upon which Gentiles could join the Church.[4] In the Council of Nicaea, “the Church had taken her first great step to define doctrine more precisely in response to a challenge from a heretical theology.”[5] The resolutions in the council, being ecumenical, were intended for the whole Church.
[edit]Attendees
All 1800 bishops of the Christian church were invited (about 1000 in the east and 800 in the west), but only 250 to 320 bishops actually participated. Eusebius of Caesarea counted 250,[6] Athanasius of Alexandria counted 318,[7] and Eustathius of Antioch counted 270[8] (all three were present at the council). Later, Socrates Scholasticus recorded more than 300,[9] and Evagrius,[10] Hilarius,[11] Jerome[12] and Rufinus recorded 318.
The participating bishops were given free travel to and from their episcopal sees to the council, as well as lodging. These bishops did not travel alone; each one had permission to bring with him two priests and three deacons; so the total number of attendees would have been above 1500. Eusebius speaks of an almost innumerable host of accompanying priests, deacons and acolytes.
A special prominence was also attached to this council because the persecution of Christians had just ended with the February 313 Edict of Milan .
The Eastern bishops formed the great majority. Of these, the first rank was held by the three patriarchs: Alexander of Alexandria, Eustathius of Antioch, and Macarius of Jerusalem. Many of the assembled fathers — for instance, Paphnutius of Thebes, Potamon of Heraclea and Paul of Neocaesarea — had stood forth as witnesses of the faith and came to the council with the marks of persecution on their faces.
Other remarkable attendees were Eusebius of Nicomedia; Eusebius of Caesarea; Nicholas of Myra; Aristakes of Armenia; Leontius of Caesarea; Jacob of Nisibis, a former hermit; and Spyridion of Trimythous, who even while a bishop made his living as a shepherd. From foreign places came a Persian bishop John, a Gothic bishop Theophilus and Stratophilus, bishop of Pitiunt in Egrisi (located at the border of modern-day Russia and Georgia outside of the Roman Empire).
The Latin-speaking provinces sent at least five representatives: Marcus of Calabria from Italia, Cecilian of Carthage from Africa, Hosius of Córdoba from Hispania, Nicasius of Dijon from Gaul, and Domnus of Stridon from the province of the Danube. Pope Silvester I declined to attend, pleading infirmity, but he was represented by two priests.
Athanasius of Alexandria, a young deacon and companion of Bishop Alexander of Alexandria, was among these assistants. Athanasius eventually spent most of his life battling against Arianism. Alexander of Constantinople, then a presbyter, was also present as representative of his aged bishop.
"Resplendent in purple and gold, Constantine made a ceremonial entrance at the opening of the council, probably in early June, but respectfully seated the bishops ahead of himself."[4] As Eusebius described, Constantine "himself proceeded through the midst of the assembly, like some heavenly messenger of God, clothed in raiment which glittered as it were with rays of light, reflecting the glowing radiance of a purple robe, and adorned with the brilliant splendor of gold and precious stones."[13] He was present as an observer, but he did not vote. Constantine organized the Council along the lines of the Roman Senate. "Ossius [Hosius] presided over its deliberations; he probably, and the two priests of Rome certainly, came as representatives of the Pope."[4] “Eusebius of Nicomedia probably gave the welcoming address."[4]
"I am assuming Nicea was an ecumenical council."
It was. Its where the Creed comes from, at least most of it.
"Who decided who should go and who couldn't go to Nicea?"
All the Christian bishops were invited because the main issue at hand was dealing with Arianism which was being preched by more than a few bishops.
"How was the council of Nicea paid for?"
I haven't a clue. Maybe at second collection at Sunday liturgies? A tax on goats?
"Who opened the council and presided over it?"
I believe the Emperor Constantine may have presided over the opening session. I know he called the Council. At least after the first session, it was presided over by +Hosius, the Bishop of Cordova and +Alexander, the Pat. of Alexandria. Interestingly, Constantine had very definite personal Arian leanings and sympathies (though he recognized the trouble Arius was causing in The Church) but the Council came down firmly against Arianism.