Im in Faction War, and get enough LP through killing War Targets and hanging around in Plexes wating for WT to arrive to fund my play*, so that I dont run missions or mine, or even game the market. Im only on a couple of times a week, and only ever for 1-2 hours, so I try to ensure that I spend the max time roaming around looking for fights. I only fly frigates, hell, I only actually fly Slashers, so each loss is about 7mill. Thats about 7,000 LP, which is peanuts in FW. I realised last night, as I dropped in unasked on a Slicer in our home system, and promptly killed it, that after 22 kills and 58 losses, I no longer get the shakes after each fight. I still make enough mistakes to fill my need for YASDs though, but they are dropping.
From what I have read, people arent short of ISK, just buy a bunch of frigates and get out and lose them, its the only way to learn.
On the mechanics of Eve PVP: there is a small amount of piloting, some small amount of module management, and a whole lot of mind games. Eve PVP is about ships and skill points in the same way that poker is about cards. It sure looks like that from the outside, but mostly it's a mind game. I have got a number of kills with my close range brawler against long range kiting ships by drawing them out of their trap and getting them on a gate or planet at 0m, rather than diving in blindly. Also, although there are some good PVP pilots out there who do fly really well, there are also a larger number who fit and fly very badly. I run Eve-Kill in parallel on my phone to check pilots where possible before I engage - if they look like psychos with 100:1 odd kill ratios, I pass them by. I had to move onto Eve-Kill from just looking at their profile, as some very experienced / old pilots flew really badly, and I realised that some had just come to FW for the LP farming, of for the fun, and hadnt been PVPing for 5 years.
I found one of the hardest things about getting into Eve PVP was 'stepping off the diving board', and accepting that I might well lose what I was flying. Easy to say "dont fly what you cant afford to lose", harder to put your ship into action and real danger. Kill boards dont help, but most days now I dont worry about the figures. An improving score is a good record of me not making as many stupid errors, but logging on to fly around for 1.5 hours not finding any fights is not a successful evening. Better to lose a ship, on MY terms, trying out something stupid than to redock again at the end of the night. Who knows, somethimes frigates piloted by 4 month newbs can kill destroyers!
EDIT: Dont wait to get into PVP. There is always one more toon skill that you need, one more module etc. In reality its a player mind-set, which just takes a few fights to get (see my 50 odd losses!). Just head off today! Fit out 10 ships, lose them, then do it again. Meta 3 and T2 guns are generally fine. T1 frigates etc
*By this I mean replace ships, not plex my account. I still pay with Paypal each month.