Hi!
I've never used either the Lady or the Baby Comp but I don't really think you need them anyway. Buy a thermometre for £3 and some paper and your good to go.
www.fertilityfriend.com is supposed to be really good for charting temperatures as well. All the Ladycomp does is remind you to take your temperatures and do the analysis for you, but sites like fertilityfriend will do that as well and it's REALLY easy to do by hand as well.
If you chart your temperatures and monitor either cervical mucus or cervix position then the method is as safe as the pill (IF you don't have sex at all on fertile days, if you do using condoms then of course it's only as safe as the condoms are). If you're interested in charting I'd invest in a book. Personally I love Tony Wechsler's "Taking Charge of your Fertility" (and I frequently say so on here, people probably think she's paying me by now). But I'm sure there are others that are just as helpful.
If you don't quite "trust" yourself and your calculations (though you'll see that it's really easy) then I'd invest in a Persona instead. Persona monitors hormone levels so gives you a back-up for your charting that's based on a different type of data. It's what I do and I'm really happy with it, as it a.) makes me feel safe and b.) tells me so much about my cycles.