@Deemarie11 I am gobsmacked that the % of posters saying YABU is so high. YANBU at ALL, to be freaked out/bothered/pissed off/anxious/stressed etc, about a man a generation older making every effort under the sun to try to make contact with you and talk to you and engage with you.
Sadly, many woman HAVE been conditioned to be NICE and be KIND even if that means putting ourselves in uncomfortable and awkward and unpleasant situations. Fuck that for a game of soldiers! 
You can bet a MAN would not be so friendly and chummy and pally if another man started chit-chatting and expecting him to engage in conversation every time he came outside! (OR if it was a woman trying to chat.) A man wouldn't do it, OR care about being polite, and engaging in conversation, if he he didn't want to. And he wouldn't be chastised by people for it for not 'being neighbourly' either. But wimmin must always be NICE and KIND! 
Then again, a man very likely wouldn't START trying to engage in conversation with another man. (Not every time he saw him in the garden, deliberately going out to chat...) Some men I know - particularly 45+ have this habit of trying to be jovial and friendly with women - a LOT more than they do with other men. Even when they're with their wife sometimes.
I know a couple of men who get arsey when the women don't respond too, and just ignore them. Even going as far as saying 'miserable cow.' The entitlement of some men is utterly breathtaking, and they do NOT like women who don't kow-tow to them, and refuse to engage/don't smile/don't simper.
Just ignore the naysayers on here. You are perfectly within your rights to be narked off and stressed and upset about this. This man is not purely 'being neighbourly' because, as I said, he would not act the same towards a man. All you can do is grey rock/ignore/roll your eyes/sigh/ignore. You owe this man NOTHING. And he has no right to demand attention and conversation.
And as for taking in packages; just say NO as you don't like having responsibility for other peoples stuff. That's what I say. I NEVER take packages in for people, and don't have them taking them in for me. Indeed, I don't want them to take them in. Some people say taking in packages is 'neighbourly.' That's their opinion. In MY opinion, it can easily become a bloody nuisance, and people will start to take advantage/not bother picking packages up/blame you if something's broken etc etc etc.
Moving house may be an option, but as a pp said, what if there's another entitled sexist man (who thinks all young women should be friendly and chummy with them,) living next door again? As I say, just ignoring him is the only option really, even to the point of being hostile. Like I said before though, a MAN wouldn't give a shit about being hostile. As I said, you owe this man NOTHING.
I thank God I have DH living with me now, because when I lived alone in a flat in a big city some 3 decades ago, I got hassled constantly by men. Followed home from the bus stop, asked out (and called a cunt/slag/frigid bitch etc when I said no,) and generally badgered to fuck by men who would NOT take no for an answer.
I even took to getting a ring that looked like an engagement ring, and a band of gold, and pretending I was married. (To try and put them off.) And even THAT didn't put some men off. (Not a stealth brag, it genuinely happened, a LOT, and I reckon many women will tell the same tale.)
You have my sympathy. I hope it sorts itself out. Can't offer much advice, but I do feel for you and am on your side.
The naysayers who are YABU-ing you have very likely never been constantly badgered by a misogynistic man inappropriately targeting a woman constantly, because he thinks he is allowed to because she's a woman and she should be NICE. Urgh! 