Welcome, I joined about a year ago with a very similar spec to you. Time poor due work unfortunately, not sure if this was all it was cracked up to be, didn't want to commit too much. wanted the opportunity for a quick blat and the odd track day.
I picked up a pre-built Tiger Supercat, 2.0 Zetec, weber throttle bodies last year for £4.5K. needed a new clutch and some tidying up but was essentially all there, so a good road car for £5k in my opinion. Massive grin factor every time you press the loud pedal!
From my research there are a lot of variables to consider which also affect cost.
Top end is Caterham style, you can see some nicely engineered vehicles but that's why they are more expensive, design/building their own suspension arms makes for a lighter/faster car but will add cost. A retired Caterham mechanic at a recent car meet also mentioned they can be more fragile on the road when you hit pot holes etc. You pretty much pick up a box of Meccano and bolt it all together (i know, not quite that simple!). Other end is like mine where many parts are sourced from donor vehicles. I have a Sierra rear suspension which then adds more weight, but keeps the cost down. You will also be cutting/adjusting more panels etc. to fit. Someone else also mentioned, be really careful about build quality. there are lots of good builders out there but as i was looking at the lower budget end, i saw some shocking examples
. Not sure I wanted to commit myself into a corner not knowing if it would hold together! I found out mine was initially build by Chester Sports Cars which seem to have a good rep, but there were still some post build bodges! Again as mentioned, these do need TLC, some more than others. How handy are you with a spanner? That may also make a difference on cost vs enjoyment. You can tinker/upgrade to your hearts content if you are that way inclined, a kit car is never finished!
last piece of advice - get a good toothbrush - you'll need it to get all the flies off your teeth!
enjoy!