I've got a paper just about to be submitted for publication on this topic, so I'll chime in here. You ask about which primer is the best for all fungi without amplifying plant (or other organisms) and which primer pair amplifies all groups of fungi evenly? Well, I have bad news for you: There isn't one. At least no one has identified a primer set that is fungal specific and amplifies across the board uniformly.
I would definitely use the ITS primers you mentioned. ITS was chosen as the "official" fungal barcoding region. I would recommend the primers ITS1F (fungal specific forward -- make sure you are using the fungal specific version that was redesigned not to pick up so many other eukaryotes -- in our studies we still have about 10% outside amplification) and ITS4 (reverse). With Illumina sequencing you may not get coverage across the ITS1-5.8S-ITS2 operon because the length varies anywhere from 600bp to 2000bp. Are you planning on using paired ends for your sequencing? If you do you should be able to assemble your ends and at least cover those fungi with the shortest ITS operon. The 5.8S is highly conserved so I wouldn't rely on it to match reads, it is one of many reasons there are so many chimeric sequencing for fungal ITS in public databases. ITS does not amplify equally for all fungi, I've particularly had some issues with amplification of the Glomeromycota.
You also mentioned the 28S or LSU (large subunit) and you can give that region a try. There are some inherent issues with the LSU also, but it's starting to be adopted for fungal amplicon studies. I personally like using the 18S (SSU) better than the LSU, but the primers are not fungal specific, so you'll get lots of other eukaryotes in your amplification. The main reason I like the SSU versus the LSU is sequence resolution across databases. I would definitely use ITS and then another one or two primers regions from there. Since you mentioned you are planning on using Illumina, you'll easily be able to use three barcodes and you should have plenty of read coverage for all your OTUs. There are other options for primers, too much for me to go into here, but that's a paper in the works right now. I would again refer you to the fungal barcoding paper in PNAS from a couple of months ago.
Databases are a big issue right now in mycology. I've spent the better part of the last two years working on a non-redundant ITS database, so if you are interested in that I can provide that to you, but I have not made it public and it's specific for my studies and may not be the best option for you. It's mainly curated from some of the great public resources: NCBI, UNITE/Pluto-F, and Lee Taylor's database are all the best in my opinion. You'll probably want to curate a database on the basis of tracking your Trichoderma and understanding how it's presence may be affecting the presence or absence of other fungal OTUs.
I wrote this pretty quickly but there are a lot of issues to discuss. I'm not sure you've thought about how you will analyze your data yet? Please feel free to contact me if you have any other questions about your fungal amplicon study that I may be able to help you with. Best of luck.
How would this work with Sanger sequencing? Any recommendations for just sequencing of small numbers of pcr products?