Let’s talk about first fruits because I think it's very important for the priesthood. It provides food and sustenance for the Levites (Numbers 18:13) (something that rabbinical tradition destroyed). And for me personally, it is also a sign of a personal prosperity. If you can perform this, it means that you are doing very good, both in the eyes of man and in the eyes of God. For me it is best summarized in the verses of Deuteronomy 26. If I could accomplish what is written there I would be very happy.
Let’s look at actual application of the first fruits command rather than just speaking of it in theory. It's something I was studying but came to a stand-still because I wasn't sure what was actually included in "firstfruits". For example, what if someone had a farm producing multiple crops in different seasons. Since the feast of firstfruits occurs in the beginning of the year, would that imply that the first fruits were to be offered from that earliest crop? How much of that earliest crop is considered the "first fruits", if that is the case? That's just a subject I've been thinking about in regard to having a farm.
Likewise, I've been considering the issue of livestock, specifically with the first born. If sacrifices are not performable, then I'm not sure how the first born males of livestock would be handled.
So as far as the first-fruits go: I think it does refer mostly to the crops, as the actual fruits and summer crops seem to be reserved for the Sukkot (festival of ingathering). I also think that the expression "first-fruits" is more of an allegoric in nature as not everyone is a crop farmer, so whatever is produced (besides the crops) in the beginning of the year is qualified as the first-fruits. I guess it can be livestock, goods, money, e.t.c. Although according to Exodus 34:22, it seems that it only refers to the crops, so I guess if you do not work with crops you would have to buy them from someone who does and then bring it as an offering.
As far as the amount of the first-fruits, I think the text say something in Numbers 28:26-31 and Leviticus 23:10-21. I think a sheaf of crops (seven times, aka counting of the Omer) would be the right answer. But I have not researched this subject in details so I'm not exactly sure.
As far as the first born of the livestock and how to handle it in our time? I'm not sure myself. But if one feels compelled to perform this commandment anyway, you can probably donate it to any "official" Levite (even though it's going to be rabbinical Levite who most likely follows rabbinic tradition and who is not technically a Levite). The word Levite mean "clinging" (to God), meaning that the Levite is someone who follows the Torah (and not rabbinic tradition). Or, I guess you you can sell it and donate money to either rabbinical Levite or to the charity or to the poor, or something like that. In the absence of the Levitical order and the sacrifices, this is the hard commandment to keep