As you mentioned it, the base is everything is halal unless it is stated by Qur'an and Sunnah it is haram. After you read the following from the Qur'an and Sunnah, I advise to refer to this website to get more details about subtypes of foods.
Prohibited to you are dead animals, blood, the flesh of swine, and
that which has been dedicated to other than Allah , and [those
animals] killed by strangling or by a violent blow or by a head-long
fall or by the goring of horns, and those from which a wild animal has
eaten, except what you [are able to] slaughter [before its death], and
those which are sacrificed on stone altars, and [prohibited is] that
you seek decision through divining arrows. That is grave disobedience.
This day those who disbelieve have despaired of [defeating] your
religion; so fear them not, but fear Me. This day I have perfected for
you your religion and completed My favor upon you and have approved
for you Islam as religion. But whoever is forced by severe hunger with
no inclination to sin - then indeed, Allah is Forgiving and Merciful.
And the Sunnah,
“Halal (the Lawful & Permissible) is clear and Haram (the Unlawful &
Impermissible) is clear. Between halal and haram lays some doubtful
things. Many people do not know whether it is permissible or not.
Whoever leaves out these doubtful things in order to protect his
religion and honor, then he is safe. Whoever indulges in these
doubtful things/matters it is very possible that he will fall into
haram, similar to a person who grazes his animals near the royal
pasture it is very possible that one day he will graze in the royal
pasture. Behold! Every king has a royal pasture and the royal pasture
of Allah is those things which have been made impermissible.”
Sayyiduna Abu Hurayrah (radhiallahu anhu) narrates that the Prophet (salallahu alaihi wasallam) said: “Allah the Almighty is pure and accepts only that which is pure. Allah (swt) has commanded the faithful to do that which he commanded the Messengers, and the Almighty has said: “O Messengers! Eat of the pure things and do right”. And Allah the Almighty has said: “O you who believe! Eat of the pure things We have provided you.”, then Rasulullah (salallahu alaihi wasallam) mentioned (the case of) a man traveling on a long ardous journey, greatly troubled and distressed, with disheveled hair crying to Allah swt, O my Lord! O my Lord! But, his food is haram, his drink is haram, his dress is haram and he is nourished with haram. How then his du’a be accepted (Muslim 1015)
Sayyiduna Abu Hurayrah (radhiallahu anhu) reports that the Prophet (salallahu alaihi wasallam) said, “A time will come upon the people wherein a man will not bother what he intakes; whether from a halal source or haram.” (Bukhari 2059)
The Prophet (salallahu alaihi wa sallam) said, “Avoid whatever you have doubts about in favor of what is not (doubtful).” (Tirmidhi)
Sayyiduna Ka`b Ibn Ujrah (radhiallahu anhu) relates that the Prophet (salallahu alaihi wasallam) said, “A body nourished with haram will not enter Jannah”. (Tirmidhi 614)
Sayyiduna S'ad (radhiallahu anhu) relates that the Prophet (salallahu alaihi was sallam) said “O S'ad purify your food (and as a result) you will become one whose supplications are accepted. I swear by Him in whose hands the soul of Muhammad lies, verily a servant (of Allah) tosses a haram (impermissible) food morsel in his stomach (due to which) no good deed is accepted from him for 40 days” (Tabrani 6395)