Depends really what you want to show, but you could give a try with a Glomeromycete or Mucormycete, should be the closest to an outgroup of basidiomycota and ascomycota.

I assumed you are dealing with sequence data. One way of doing this is leveraging on BLAST to figure out which one is the closest sister species not in INGROUP.

Yes, you could choose from a different division, for example Batrachochytrium that belong to Chytridiomycota.

Even more distant species like Rozella allomyci that belong to Rozellomycota

You should probably test the impacts of different strategies, including no outgroup at all.

You may check this paper and relevant references within: Article Architectural instability, inverted skews and mitochondrial ...

Thank you for answering, it's been awhile since I originally posted and then with the current world situation I have been busy in other aspects so hadn't gotten much chance to check back in. I appreciate the feedback and advice! This is for my MSc work analysis portion so the answers gave me some options to think about.

I am quoting a Viralzone crash-course on phylogenetics:

"What to choose for the Outgroup?There are two requirements for the outgroup:

• It should absolutely not belong to the group under study, otherwise the tree's topology will be hopelessly wrong
• It should not be too distantly related either, because it must be aligned with the other sequences. If it is too distantly related, the alignment quality may suffer.

In conclusion, a good outgroup would be a member of a sister clade. For example to produce a phylogeny of FMDV, one would choose another Picornavirus. But the sister clade of the group under study may not be known, and it may be safer in this case to choose a more distant relative."

You can find it here:

https://viralzone.expasy.org/e_learning/phylogenetics/content.html