Pilot reported confusion regarding VFR reporting points while arriving into BFI airport.

Narrative

VFR flight following from ZZZ to BFI was initiated by Whidbey Approach; handed off to Seattle Approach; handed off to BFI Tower when I was north of Fort Lawton at about 2000 ft MSL. I checked in with the ATIS and was told to fly over Green Lake and use the Green Lake transition. I reported 'Unfamiliar with Green Lake and unfamiliar with Green Lake transition.' The Tower Controller said 'You're supposed to know the routes on the TAC chart. Green Lake is 3 miles ahead on your present heading' or equivalent verbiage. This was wrong; Green Lake was about 3 mi due east (I figured out later). I continued straight ahead; WEST of downtown Seattle; on what appeared to by a nice extended right downwind for Runway 34L/R at KBFI; I was expecting 34L since Aircraft X flies more or less like a jet. After I passed downtown Tower said 'you're supposed to be following the other shoreline' and I asked 'you want me over the west shore of Lake Washington?' and got a 'yes' so turned left to comply. Tower said 'You're cleared to land number 2 for 34R; follow the traffic on a half-mile final.' (I didn't hear 'right'; but I think he said that; I was thinking 34L.) I read back 'follow the traffic on final; cleared to land' and I saw Aircraft Y traffic that looked high for 34L but assumed he was landing long. Tower said 'Please tighten up your downwind' and I replied 'I'm turning base right now.' I lined up for 34L -- note; ADS-B In traffic was working fine; and my copilot was helping me spot traffic -- there was no traffic approaching 34L; so no conflict. On 1/4mi final; Tower said 'Aircraft X; you're cleared to land on 34L' which I acknowledged; apologized for my error; and landed. Rolling out; I apologized again and asked if I needed to call anyone or report anything; and Tower said 'No; we just turned it into a non-event.' On Ground; I mentioned that Aircraft X would have difficulty with 34R (meaning; the tight turn from downwind to base to final) and they let it drop. ... Contributing factors (1) Last year; flying practically the same flight; I was NOT asked to use a transition route. (2) Haven't seen a TAC chart in years; everything's on the 6 different databases used on each of 4 Garmin boxes. (3) BFI Tower might have been a relatively new guy overloaded by weekend VFR traffic? Gave me one wrong vector and seemed to have a one-size-fits-all notion of VFR traffic (they're all Cessna 172 type equivalents)? (4) I have the opposite bias; everyone should know that Aircraft X flies fast and doesn't turn tight and should be handled like a jet. (5) So... I was not cognitively prepared to hear '34R' and completely missed that clearance and did not read back '34R' (6) Tower didn't force me to read back the runway clearance; and didn't reiterate it. OK; there's more. After landing I looked up the TAC chart on Skyvector.com (of course the FBO didn't have one; no one carries paper charts any more). I carefully studied the VFR transition routes for departure. The main graphic on the VFR back side of the TAC shows the routes in and out of SEA. On the right hand margin are two smaller graphics with 18 transition routes for BFI; depending on coming/going; landing direction; and origin/destination. They use some dedicated reporting points mapped on the small BFI graphics; some common reporting points mapped on the main graphic; and some that aren't mapped at all like Renton Concrete Recycling; Lincoln Park and Southcenter (which is a shopping mall area). I studied the Rainier route and queried Clearance Delivery; asking for VFR flight following. 'We don't coordinate flight following on the ground; you have to call for it after you leave your transition route.' Well do you have a frequency? 'Yes; Renton Tower is XXX.XX and then Departure will be YYY.YY.' Okay; do I need a transponder code? 'Oh yeah; you need to squawk XXXX.' I would evidently not have been given the code until takeoff; or after; unless I'd asked for it. I navigated this route adequately and tried to get flight following; but Departure was overloaded. Recommendations: (A) I recognize that BFI is tricky airspace; but those obscure and unmarked reporting points have got to go. (B) Just like SoCal recently did with its pet TEC routes that were on back pages of the Chart Supplements; they found a way to make procedures out of them that get inserted in the navigational databases. So if VFR transition routes are going to be demanded by Towers; then get them on navigational databases; not on the margins on the back side of the TAC charts. (C) I know that the FAA's having trouble hiring and retaining controllers; but they can't assume that every arrival is a local area expert. If someone's approaching at 200 kt; they probably won't mind a 10-mile vector over some very recognizable landmarks like Lake Washington north end or south end; Lake Union; the Space Needle; downtown Seattle; Renton airport; etc. Also; using SR-167; a small highway unlabeled on any of the graphics is just dumb. Google also does NOT label most small highways; so if you don't DRIVE on it; you'll have to dig up a Rand McNally road atlas to figure this out. FINALLY I called up a local pilot to ask about this; and he had no idea knows most of the landmarks but didn't know about the transition routes; couldn't find a TAC chart electronically until I showed him where; and is now studying. Sorry; all that info needs to find its way onto nav databases.