Owning & Driving the same TR6 for 31 yrs I agree the easiest immediate improvement is tires. Fitted with the great looking but horrible as far as handling goes hard as a rock compound 185 michelin redlines from the 70's (I might add they were worth there weight cause they lasted 4ever interms of the mileage you got out of a set even worn to near slick condition) the 6 was skiddish, all over the place and took every bump or crack in the road as if riding on cobble stone, as well as a butt puckering episode on certain cambers, continued after suspension rebuild 1990 using rubber bushings, I'd run 30 psi for long distance trips 24 psi/front 26-28 psi/rear local crusin'
Handling got a little better with install of Koni shocks in 80's then tube shock conversion during that time Pirelli made a 185 series tire for Jag, 5" wide 3/8" white wall with pirelli in white at a cut out, I used a tire shop grease type crayon to paint the strip red, got a set of those the difference in handling, ride and grip in cornering was remarkable as it was a softer compound, they only lasted 3 yrs & 20 some thousand miles.
Fast forward to the 90's modern rubber coker classics, looked great on the 6 close to original look of 185's (use to be able to slide 3 fingers between top of tire and front fender well) coker's 5-1/2" wide 205/R78 (strangely same size tire I ran on a '78 Cadi Seville) I could slide 2 fingers in. That was the only change since suspension rebuild but the ride, handling was sustainial both control and comfort. Intended to get another set until I saw and asked owner whether or not a certain 206/70 Redline rubbed when engaged in a full locked turn or rough road cruising. Since 2003 running Redlines (always will on my 6 as long as we're 2gether) spax adjustable's front/rear quick-steer race/rack and Good Parts adjustable trailing arm brackets to maintain negative camber in rear (no leaning in at the top under load or weight nor tipping out at top on certain road cambers, but instead tires remains in vertical position under all driving conditions. Diamondback Tires 205/70/15 allows 2 fingers fit between top of tire and wheel well, 6" of rubber on the ground, softer and at same time gripping ride, no more dreaded squealin' like a stuck pig when an attempt to turn is made period, whether on concrete in a parking garage or sampling a little adrenaline on a autoX, tires definitely the 1st major improvement, but to help insure the life of that investment, one might want to upgrade/rebuild suspension. I'm a more I get, the more I want guy that drives to ride, more than to race/speeding, perfer long distance 70 mph cruisin' and twisty/curvy roads, tried comp, later 6 and a couple other springs, found set near year of my 6 that maintains how it set from factory, so I guess you could say my upgrades remain close to factory then super modified, engine/exhaust not on steroids, suspension/ride not super stiff, TRuly a Passion to Drive a well kept/well maintained 6. Ongoing Luv Affair!