I started with a lasher and had little difficulty in killing pirate buffalos (which drop loads of supplies) and seeing off hounds (often using missiles). I admit I did leave it on the default 50% damage because I wasn't looking for a tooth and nail fight up above survival level, but most new players apparently don't know this setting exists, so I think the comparison is still fair.
I think part of the problem may be that the beam wolf is actually quite hard to use now - I tried it as well but it was noticeably tougher. It really is a -support- layout now... Perhaps one set up like the pulse laser wolfs from the Wolf Pack mission would be a better starting ship than the gravi-beam and taclaser one?
Since then, I -have- been playing with frigate swarms, and they're great. Cheap to deploy, so you can use them in nice big chunks, very cheap to run (10 frigates that you aren't actively fighting with will cost you about 2 supplies per day, and you can get like 50-60 from an average small pirate fleet - which you can probably kill with only 3 or 4 of those 10 frigates), and nicely effective at killing stuff if you set them up right. People who want longer duration frigates should however look to the lowtech and midtech frigates, especially the Lasher which lasts ages. The Wolf and the Hyperion are both a fair bit more expensive than 'normal' frigates, especially the hyperion - I haven't tried a tempest yet but I don't think they're quite as bad - use these as strike vessels or reinforcements when things aren't going so well.
Frigates also mean you can run from anything too big, and chase down anything slow and weak like buffalos without much difficulty - but you do run into the problem that in any close fight, you're going to lose some frigates and some crew will die. If you pick your fights well enough you'll make this money back, but if not, you can lose a frigateswarm horrifyingly quickly - knowing when to run is probably a good idea (I'm actually bad at this) because frigates should be able to run away from everything on the escape map without too much difficulty. I can never catch Hounds, thats for sure.
Regarding fighters... yeah, they cost way too much. Someone said they thought it was a bug, because the values seem appropriate per-wing, but are actually applied per individual fighter. Either way, 2-fighter wings like thunders or xephos aren't as bad.
(Alex, do you care to comment here on whether fighter supply is working as intended, slightly broken and will be rebalanced, or actually bugged and will be calculated differently? There's maybe a couple of threads about it in suggestions or bug reports also, if here isn't the best place)
Overall though I'm really enjoying the new release - I haven't found it unduly difficult, if anything it's easier as well chosen fights can now provide a lot more credits a lot quicker through selling supplies, but there are probably more potential pitfalls if you do start failing too much. I love the new logistics changes in general... the UI is okay, sometimes I preferred the old one (buying/selling ships is the main one), and I've no idea why the F1 tips aren't just always there, or indeed why the full logistics panel doesn't always display - can we get those as toggle options perhaps? All in all though, worth the wait!