As Benny Hofer said there is a few cool things to check out. I sold my Clio Gordini to my 19 year old cousin Cody so it's still doing the rounds. It has Akra exhaust (7kg weight delete vs standard), K&N panel filter, RE003 tyres, Quaife LSD and Powerflex road series engine & gearbox mounts. It's a well sorted car worth checking out
I wish I knew about this forum before I started out doing light circuit work like you described as I learnt from my mistakes which I will share with you.
1. The very first thing you need to do before you head on track is go and buy Redline MTL75-80 gear oil from the automotive retailers. It will cost you $120 for 3.78ltrs and DIY or mechanic to install. Plenty of you tube videos to help you DIY but search Clio 197 to make it easier. TL4 gear box takes 2.5ltrs approx. When you go on track at barbs with long straight and plenty of wide open throttle the engine particularly gets hot and transfers all that heat to the gear oil making the old gear oil breakdown. No matter if you can rev match down the box them standard OEM synchro’s rings made of cheese will start to fail. Change your gear oil every 2 years and you can't go wrong. Damage the synchro’s like it did and you need to budget $3k to put it right.
2. Second thing to do is go on the KTEC UK site or there is a Powerflex engine mount distributor on the east coast, or eBay and order the top dog bone "Powerflex road series" (usually purple & yellow in colour) bushing. https://www.ebay.com.au/itm/Powerflex-Renault-Clio-Sport-Mk3-197-200-Upper-Engine-Mount-Arm-Bush-/163934244847 This is important as if you can push your engine front to back of the car and it has slop it need replacing. If not you can damage the header pipe flexy joint which is a whole new header if that fails. While your at it... the middle engine bushing and lower should be replaced as well as the gearbox mount. The lower engine bushing/mount are prone to cracking under the weight and stress of the engine and cars dynamics. Do all of this and the benefit is better more direct handling. Car will feel new again and best money spent in my opinion. I used Charlie at Bridgestone Select in Morley to install all my Powerflex bushings as he does all my cars wheel alignment geometry. He used to set up the Clio for 1 deg toe for turn in at Autokhana.
3. Spend your money on regular oil changes at 5,000kms intervals. It's proven that just changing engine oil from old to new pics up a few ponies as old oil has debris that robs horsepower. I prefer Castrol Edge 5w-40 as its well priced on special and one of the biggest oil companies in the business. Your engine will love you for it and serve you well in return. Make sure you keep an eye on cam belt service. Needs replacing every 4 years.
4. Change your brake fluid to Castrol Performance DOT4 and ensure your pads have heaps of meat. For the old track day no need to upgrade brakes straight away as they car is light on over braked compared to other hot hatches. No need to waste money at the start, the above is more important.
All the above will cost you bugger all in the grand scheme if things and allow you to have fun and use your car with what it was designed to do which is carve corners.
Now the expensive wish list - As far as performance mods I think the best thing was when I fitted the refurbished KTEC TL4 gearbox with uprated brass 3rd & 4th synchro’s rings I opted to have KTEC fit the Quaife LSD. It just puts down all that power to the road and allows you to be greedy and pick up the throttle early mid corner keeping you glued to them GTR and M badges you mentioned above My refurbished TL4 box with new uprated brass synchro’s internals, LSD, new OEM clutch, new slave cylinder landed into Perth with gov duty was $4K... Ouch!
I do believe the car will benefit from light breathing mods. Another mate with a Clio Angel & Demon fitted the KTEC exhaust because bang for buck it was high quality finished for the price. Budget for $1,200 AUD landed into Perth. It helped free up the engine and was quite a weight delete benefit as well compared to the heavy OE system.
Don't spend crazy dollars on pulling off the head, polishing & porting and fitting CAT cams. It's huge dollars and the benefit is not there in my opinion. I reakon your better off changing the battery to a light weight lithium and removing the rear bench seat which will take 30kgs out of the car. KTEC sell a nice carpet to cover the whole rear hatch floor once the bench is removed.
Spend your money on good tyres. Good tyres provide better laps times than any other mods. It's hard to find a tyre that performs well both on road and track. On a budget the for UHP Performance Passenger car tyre category Bridgestone RE003 when purchased on special (buy 3 & get 1 free) will cost you $650 fitted for your Clio 215/R17/45P. I bought 2 sets over the ownership of the Clio Gordini. They do an extra lap or 2 over say a Michelin Pilot Sport 4 or a Conti Sport Contact 6 starts to get over heated and you feel the car start to squirm and move around.
Next step up from that is road legal weekend track tyre. There is 2 I know of to choose from that guys use at my Autokhana club. Yoko AD08R they will cost you $300 per corner only available from John Fowler in Osborne Park email@example.com he is a legend for car setup for motorsport and a really nice guy. Or Bridgestone have the RE71R which will cost you $250 per corner.
You have already identified the last thing you need. Time in the saddle and an instructor next you with every opportunity you get