The Linn LP12 will presumably work satisfactorily with any good tonearm, although I personally did not find that to be the case during the (short) period of time I owned a LP-12. (I sold my LP-12 and replaced it with a VPI HW-19 Mk4.)
If you want to consider non-Linn tonearms, then you should definitely include the Rega RB-900 (or RB-1000 if you are fortunate enough to find one on the used market). The top-of-the-line Rega tonearms are among the best in high-end, and offer excellent performance and value. The RB-900 sells new for $1000, but can be found used for around $650. The new $1600 RB-1000 (which I recently acquired) is stunning well-made, and I think is fully competitive with a lot of tonearms in the $2500-3000 bracket.
Several reviewers for different audio mags have commented that Rega might not have developed the RB-900 due to cost if they were doing so today. The design for the RB-900 was done a number of years ago, so the development costs are now fully amortized. The casting for the tonearm itself was very expensive, and requires very skilled workers to do the finishing. The single-piece tonearm/headshell make for a very rigid platform, and the ball bearings used in the pivot are first-rate. The RB-1000 takes all of this to an even higher level, and at present Rega has only two craftsmen who are sufficiently trained and skilled to do the final finishing (hence, limited availability and relatively high price).
The only "downside" to these two Rega arms (for some people) is the lack of VTA. The tonearms do come with stainless steel spacers which raise the base of the arm, and I have found this to be quite satisfactory. I do not obsess about changing the VTA for every LP I own. With the spacers under the base, I have found the VTA is optimal for about 85% of the LP's I own (it could be tweaked a bit for the 200-gram LP's).
