My suggestion (and what I do) would be to continue using DynDNS, and create a subdomain for
home.example.com and make a
myhouse.dyndns.com (or whatever your DynDNS domain name is). This gives you the flexibility of using your own domain name with the ease of updating of DynDNS.
Personal example: (the .doesntexist.org address is my DynDNS address)
0 09:37:13pm ~ $ dig woodcrest.thepurplepixel.org
; <<>> DiG 9.4.3-P3 <<>> woodcrest.thepurplepixel.org
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 28814
;; flags: qr rd ra; QUERY: 1, ANSWER: 2, AUTHORITY: 0, ADDITIONAL: 0
;; QUESTION SECTION:
;woodcrest.thepurplepixel.org. IN A
;; ANSWER SECTION:
woodcrest.thepurplepixel.org. 3600 IN CNAME thepurplepixel.doesntexist.org.
thepurplepixel.doesntexist.org. 60 IN A 22.214.171.124