I am basing myself mostly on the work "Prince Henry 'the Navigator': A life" by Peter Russel, with the addition of this accessible article "Another 1415: Portugal’s military landscape at the time of Agincourt" which would be an interesting read to you. Two works corroborate in all aspects.

I am not sure where the number 48,000 comes from, likely from some Chronicle or other account that may exaggerate things for effect? But for estimates of number of Portuguese troops both of the above works quote two contemporary accounts / letters that state the Portuguese army to be 19,000 or 32,000 soldiers respectively.

The number 19,000 is given by one Ruy Diaz de Vega, an agent in the service of Aragonese king, in a private communique where he informs his king on the preparations Portuguese are making, mere weeks before the launch of the operation. He got this number from official document and pay roles of the Portuguese to which he somehow got access to. He also lists the troops by type: "5400 men-at-arms, 1900 mounted bowmen, 3000 unmounted bowmen, and 9000 footmen".

The number 32,000 is found in an official letter written by the Portuguese "alferes-mor (royal standard-bearer) João Gomes da Silva", in a letter to archbishop of Compostela, which lists "270 sails, 7000-7500 men-at-arms, 5000 bowmen, and some 20,000 footmen".

Of the two numbers, the authors of the works I listed above tend to accept the first as more likely and accurate. The second one comes from the letter to a archbishop in another country (Compostela being in Castille-Leon) and that may be a sort of exaggeration or brag to play themselves up in the eyes of their neighbors / adversaries.

Both of the writers also compare that number with some accounts from 1411 where king Joao I estimates that he can organize his standing army around 3200 "lances" / men-at-arms gathered from vassals, minor nobles, and military orders; and several thousands (cross)bowmen taken from town militias under the existing systems. Footmen aren't mentioned, but several examples from some battles show that usual number of footmen was between 1.5x-2x the number of men-at-arms.

All this meant that the estimate, especially the first one, are plausible sort of. There is still a minor issue of discrepancy between the number of 3200 lances estimated for the standing number and almost double that number of 5400 men-at-arms for the Ceuta campaign, but the number may be specifically increased due to the campaign, by recruiting the maximum you could (while for standing army it didn't have to be the case). The King also called for assistance and manpower from other nations, like English and French but only very minor number came from those. There could be a number of knights coming from other Spanish kingdoms and elsewhere, but if that happened can't be confirmed by anything.

As to how the Portuguese financed it - it is hard to say. Likely going into debt, and hoping loot and ransoms will pay it back. The kingdom was small and impoverished by previous wars. On this subject Peter Russel gives the following remark:

the Portuguese crown obviously could not afford such an enterprise, but history shows that even desperate financial stringency rarely proved a serious impediment to a medieval ruler now determined, as John I was, to make war.