This is part of our office desk (SWMBO's side as it was less cluttered than my side). Forest Red Gum and Tallowwood:

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Full of gum veins and other defects, it was awkward to catch the level of sheen particularly with the morning sun creating havoc through the window. The finish is two coats of matt varnish (that alone should appeal to you ) followed by Scandanavisn Teak Oil rubbed in with either steel wool or a scourer. I have used this extensively over the years for many purposes and it is also the finish I use for my hand saw handles. I would describe it as a high satin level of sheen. The use of steel wool or scourer in conjunction with the oil after 48 hours for hardening gives a silky smooth finish.

Very light sanding is done between the two coats of varnish applied at 24hour intervals. A further refinement would be to first coat the timber with a 50:50 mix of mineral turps and varnish to achieve a higher penetration into the timber before sealing with the two full strength varnish coats. Any brand of matt varnish is probably ok and I think Danish oil can be substituted for the Scandanavian Teak Oil as really it is just a lubricant for the rubbing medium.

I am wary of full gloss finishes (varnish, shellac/French Polish etc) as the surface has to be absolutely perfect for that. Full gloss makes even minor imperfections stick out like you know what canine parts.

Regards
Paul